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Introduction To Business Analytics Using Simulation 1st Edition Jonathan P. Pinder - Solutions
A local dairy manufactures ice cream as part of its operations. It supplies ice cream to 75 local restaurants. The dairy makes a 5-gal size of ice cream for these restaurants. Fifteen of these restaurants are frequent customers and order ice cream about 60% of the time (about 6 out of 10 days).
A tire manufacturer has a contract with a large rental fleet of cars. The manufacturer guarantees tread-life. If a tire fails before the guaranteed number of miles, the company offers $1.25 refund for every 1000 miles less than guaranteed. The unit contribution of a tire is $.50/1000 miles. The
Weekly demand (order size in gallons) for milk at a dairy is normally distributed with an average demand of 1,250 gal and a standard deviation of 150 gal. How much milk should be produced each week if the selling price to grocery stores is $1.85/gal and the cost to the dairy is $.65/gal?
A local dairy supplies 15 local restaurants with ice cream for their desserts each week. Each week, on average, 30% of the restaurants order a gallon of vanilla ice cream. The ice cream is produced once a week before orders are taken and cannot be stored for longer than a week(unsold must be
On Friday evening, the manager of a small branch of a car rental agency finds that she has five cars available for rental on the following day. However, she is able to request delivery of additional cars, at a cost of $35 each, from the regional depot. Each car that is rented produces an expected
A buyer for a direct mail (catalog) merchant is trying to decide how many sweaters of a particular SKU should be purchased for the upcoming season. The cost of the sweater to the merchant is $30.00 and it sells for $58.95. Sweaters not sold during the upcoming season are sold at a 50% discount
Demand for a perishable product is estimated to have a Normally distribution distributed with a mean of 336 units per week and a standard deviation of 48 units. The unit variable cost is $36.a. How many units should be ordered to if price = $40?b. How many units should be ordered to if price =
Triangle Developers is a commercial land developer that specializes in building shopping centers and wants to develop land near Charleston, SC. Triangle expects that the Net Present Value (∼ profit over time in today’s dollars) without the cost of the land will be $65,000,000.In other words,
An online/catalog retailer will sell Adirondack chairs this season. The retailer purchases the chairs from a supplier at a cost of $175 and will sell them for $250. Demand has been forecasted to be 2000 chairs this season with a standard deviation of 10%. At the end of the season, the company will
Once prices and restrictions have been determined for a specific flight, it is revenue management’s responsibility to determine the number of seats available in each fare category.An aircraft seat for a particular flight is a highly perishable commodity; once the plane takes off, the unsold
A company is bidding to supply computer servers to a large bank. The company expects the competitors’ bids to be Normally distributed with an average of $2,500,000 and a standard deviation $350,000. If the bid is won, the total cost of completing the order is $1,850,000.a. Calculate the optimum
A company is bidding to supply parts to a computer manufacturer. The competitor’s bids are estimated to be Normally distributed with an average of $260,000 and a standard deviation of$15,000. If the bid is won, the total cost of completing the order is $185,000.a. Calculate the optimum bid using
It is uncertain as to what a competitor will bid on an upcoming contract to supply parts to Boeing. The bid is almost certain to be between $250,000 and $300,000.a. Write the probability function, f(x), for this random variable. Is it a pmf or a pdf?b. What are the average and standard deviation?
An insurance company has introduced a policy that covers certain forms of personal injury with the standard payment of $100,000. The yearly premium for the policy is $25. On average 100 claims per year lead to payment. There are more than 1 million policyholders. What is the probability that more
Assume that about 5% of the people who make airline reservations on a particular flight do not show up for the flight. Thus airlines often make more reservations than the airplane will hold. If the airplane holds 100 passengers, how many reservations can the airline make and still be 90%sure that
A manufacturer of air compressors examines the quality of the finish for blemishes that do not affect the performance (superficial blemishes). Units with such blemishes are sold at a discount.The motor housings for compressors have a 2% rate of superficial blemishes. What is the probability that 4
An oil company purchases crude oil for use to manufacture gasoline by bidding in a commodities market. Currently, bids for crude oil are Normally distributed with an average of$68.15 per barrel with a standard deviation of $1.75.a. What is the probability of winning if you bid $68.00?b. What is the
A supplier of trees to home and garden/hardware chains claims that 90% of the supplier’s dogwood trees survive the first year.a. What is the probability distribution for the survival of a single tree?b. What is the probability distribution for the number of trees surviving from a batch of 250
A company is bidding to supply computer servers to a large bank. The company expects the competitors’ bids to be Normally distributed with an average of $2,500,000 and a standard deviation $350,000.a. What is the probability of winning if you bid $3,000,000?b. What is the probability of losing if
A plant that bottles propane used for grilling uses an average of 125,000 ft.3 of propane a day with a standard deviation of 15,000 ft.3a. What is the probability that production for a day will exceed 135,000?b. What daily capacity would satisfy daily production 95% of the time?c. What is the
Demand for a particular SKU of khaki pants at an online/catalog retailer is forecasted to be Normally distributed with a mean of 1,200 units per month and a standard deviation of 100 units per month.a. What is the probability that demand will exceed 1,000 units next month?b. What is the probability
A manager has forecast the budget for a particular department to be $1,250,000. Based on past data, deviations from the budget are known to follow a Normal probability distribution with a mean of 0% and a standard deviation of 5%.a. There is a 95% chance that expenditures will be between what two
A contractor regards the cost of satisfying a particular contract as having a Normal probability distribution with a mean of $500,000 and a standard deviation of $50,000.a. There is a 95% chance that the cost will be between what two values?b. What is the probability that the cost will be within 5%
Interpolation: The marketing department of a clothing retailer produces mail order catalogs and is evaluating the effectiveness of their mailings. The table below gives the number of catalogs mailed out and the sales corresponding to those catalogs.Catalogs (1000’s)Sales ($1000’s)5 50 10 125 15
A consulting firm has an average of six new contracts of a specific type of project per month.a. What is the probability of not obtaining any new projects of this type during a month?b. What is the probability of obtaining five or six projects in a month?c. What is the probability of obtaining more
Demand for a specific model of car at a car dealership is Poisson with an average of four per month.a. What is the probability of not selling any of this model during a month?b. What is the probability of selling more than three of this model during a month?
An analyst for a propane company has analyzed demand for tanks of propane over the previous 5 years and noted a strong rise in demand during months in which there are severe storms(hurricanes, tornados, etc.) due to people without power using propane to cook and heat with propane. Furthermore, the
An E-commerce site receives an average of 6 orders per minute. Assume orders arrive in a Poisson manner.a. Use simulation to compute the following probabilities: P(Orders = 6), P(Orders > 6), P(Orders < 6).b. Determine the average transaction time and average waiting time for an order assuming an
An insurance company has introduced a policy that covers manufacturing companies for a specific injury to its line workers. The probability of a worker having this injury is 1 in a 1,000.The company has 12 workers.a. Why is the Normal approximation not appropriate?b. What is the probability that
A FedEx contractor owns 50 trucks in a region. 20 of the trucks are relatively new and each of these trucks has a 5% chance of not being in service on any day. 10 trucks are older and only have a 90% chance of being in service on any day. 20 trucks are much older and have a 20% chance of not being
Assume that about 95% of the people who purchase tickets on a particular flight show up for the flight. Thus airlines often make more reservations than the airplane will hold. A small commuter jet has a capacity of 10 seats. Twelve tickets have been sold for this flight.a. What is the probability
Two basketball teams are playing a best-of-seven championship series. One team has a 60%chance of winning any single game. Assume that the games are independent (hmm?). What is the probability that the team with the better chances wins the series?
Suppose you roll a single 6-sided die (D6) and then flip that number of pennies.a. Construct a simulation to estimate the probability of each outcome.b. Compute the probability of each outcome.c. Compare the simulation probabilities (empirical) to the theoretical probabilities.
Create a simulation of flipping 100 pennies. What is the probability distribution for the number of heads?
As a sales promotion, a soft drink manufacturer places winning symbols under the caps of 10% of all soft drink bottles. You buy a six-pack of soft drinks, what is the probability that you will win a prize?
Monthly demand for a particular model of car at a car dealership is uniformly distributed between 0 and 20.a. Write the probability function, f(x), for this random variable. Is it a pmf or a pdf?b. What are the average and standard deviation? What is the managerial interpretation of these?c. What
A fruit and vegetable wholesaler buys strawberries at $20 per case and resells them at $50 per case. Because the wholesaler markets primarily to “natural” grocery stores, no preservatives are added to these strawberries. Thus, any cases not sold on the first day are given to a local food bank.
Weekly demand (order size in gallons) for milk from a dairy is listed in Table 6.15. Assume that orders are in lot sizes of 25.a. Construct a contingency (frequency) table and a probability (relative frequency) table for demand.b. Construct a decision tree.c. How much milk should be produced each
Costco must determine how much milk to order to meet demand for the upcoming week at a specific store. Costco buys milk for $2.00 per gallon and sells the milk for $2.35 per gallon.Demand for 50 previous weeks at that store is shown in Table 6.14. Note that orders are delivered in trays of 50.a.
Two construction companies, Pine Grove Construction (PGC) and Eagle Construction, are bidding against one another to construct a new community center. PGC estimates that it will cost$1,260,000 to build the community center. Based on previous contract bidding, PGC believes that Eagle Construction
A small resort hotel has 10 rooms and rents them for $120 per night. Demand for rooms for 80 nights is given in Table 6.12.a. What is the optimum size (number of rooms) for the hotel?b. Construct a simulation to determine the optimum decision.c. Construct a decision tree to determine the optimum
A buyer for a chain of department stores must place orders for athletic shoes 6 months before the shoes will be sold in the stores. At this time, the buyer must determine the order size for a particular style of running shoe for the upcoming spring season. Each pair of this style costs the
A small resort hotel has 10 rooms and rents them for $120 per night. The frequency of demand for rooms is given in Table 6.10; for example, there were 4 days in which only 8 rooms were rented.What is the average demand?a. What is the average number of units rented in a day?b. Construct a simulation
On Friday evening, the manager of a small branch of a car rental agency finds that she has 4 cars available for rental on the following day. However, she is able to request delivery of additional cars, at a cost of $25 each, from the regional depot. Each car that is rented produces an expected
A contractor has to decide how much to bid for a construction project. It will cost $4,000 to prepare the bid. This cost would be incurred whether or not the bid was accepted. The previous winning bids for similar projects have been (in $1000s): 80, 60, 70, 60, 60, 80, 80, 60, 80, 80, 50, 50, 60,
Two construction companies, Pine Grove Construction (PGC) and Eagle Construction, are bidding against one another to construct a new community center. PGC estimates that it will cost$1,260,000 to build the community center. Based on previous contract bidding, PGC believes that Eagle Construction
A commercial land developer specializes in building shopping centers and wants to develop some property near Blowing Rock, NC. In order to develop the land, the developer must bid to obtain the property. The developer has estimated the NPV without the cost of the land to be $20,800,000.The
A company is bidding to supply cardboard boxes to an online retailer. The competitors’ bids are equally likely to be above or below $160,000. The competitors’ bids are nearly certain to be between $145,000 and 190,000. It is estimated that there is a 25% chance that the bids might be below
A company is concerned about the amount of usable components it receives from a supplier. For a set up cost of $800 and a variable cost of $60 the company can make their own parts. The company can buy reconditioned components in batches from a supplier but the number of usable components varies
A convention with 1200 attendees is scheduled to take place in November in Boston. A at a price of $450, approximately 480 attendees will stay at the convention hotel. Based on previous demand data analysis, a $20 price change results in a 15% change in demand. Based upon the market value and
Demand for a specific $1000 passenger cruise booking is 1000 passengers. A $50 price change results in a 10% change in demand. Fixed cost of operating the ship is $250,000 and the variable cost for a single passenger is $375. Due to the average amount of profits for a booking due to food, drinks,
A commercial land developer specializes in building shopping centers and wants to develop some property near Hilton Head, SC. In order to develop the land, the developer must bid to obtain the property. The developer has estimated the NPV without the cost of the land to be $15,500,000.The developer
An online/catalog retailer will sell Adirondack chairs this season. The retailer purchases the chairs from a supplier at a cost of $175 and will sell them for $250. Demand has been forecasted to be 2000 chairs this season, but is not known for certain and could range anywhere from 1000 to 3000
For a batch of 50 reconditioned parts, the operations manager estimates that: (a) half the time that at least 85% of the components in a batch will be usable; (b) at most 98% of the components will be usable; (c) there will be at least 75% of the components will be usable; (d) 75% of the time at
A company is bidding to supply cardboard boxes to an online retailer. The competitors’ bids are equally likely to be above or below $160,000. The competitors’ bids are nearly certain to be between $145,000 and 190,000. It is estimated that there is a 25% chance that the bids might be below
A company is bidding to supply cardboard boxes to an online retailer. The competitors’ bids are equally likely to be above or below $160,000. The competitors’ bids are nearly certain to be between$145,000 and 190,000. If the bid is won, the most likely total cost of completing the order
What is the probability of making everyone happy?
You’re one of a hundred people standing in line to get onto an airplane that has 100 seats. There’s a seat for every person who’s in line, and each of you has a boarding pass for your assigned a seat. The first person to walk onto the plane drops his boarding pass and, instead of picking it
The probability of rain, as given in the newspaper, for the next 3 days is 30, 20, and 30%. What is the probability of getting some rain?
You have a coin that you know is biased; one side has a higher probability of turning up than the other side. Describe a process by which you can use this coin to make fair decisions (decisions with equal likelihood).
In Catch 22, a novel about World War II bomber pilots, Joseph Heller states that the probability of a B-17 getting shot down on any given mission is 2%. The author states that since the required number of missions was 50, there was a 100% chance of getting shot down; how do we know this is wrong,
In a room with n people, what is the probability that two people celebrate their birthday on the same day of the year? How large should n be so that the probability of a shared birthday is greater than 50%? Assume 365 days per year. This problem is well documented as The Birthday Problem.
A company is considering whether to market a new product. For the sake of simplicity, assume that, if this product is marketed, there are only two possible outcomes: success and failure with probabilities p and 1 − p, respectively. If the product is marketed and fails then the company will lose
A product manager must determine whether her company should market a new brand of toothpaste. It has been estimated that if the new product succeeds in the marketplace then the company will earn $1,800,000 in profit from the sale of the new toothpaste. If the product fails, the company expects that
A customer has applied for a 1-year loan of $100,000 at an interest rate of 10%. If the bank does not approve the loan application, the $100,000 will be invested in bonds that earn a 6% annual return. Currently, if the loan were to be approved, the bank believes there is a 4% chance that this
There are two people going to a concert that starts at 9:00 p.m. Each person will arrive at the concert independently between 8:00 and 9:00 p.m. Assume their arrival times are independently uniformly distributed over 8:00–9:00 p.m. Whoever arrives first will wait for the other one outside, so
One percent of people at age 40 who participate in routine cancer screenings have cancer. 80%of people with cancer will get positive screenings. 10% of people without cancer will also get positive screenings.This type of question has been asked of physicians and medical students with very small
Automobile state inspections are required annually in order to register vehicles for license plates and license plate renewals. Suppose that 18% of all cars inspected have problems that need to be corrected. State inspections fail to detect these problems 12% of the time. On the other hand, an
Marketing research firms often contact respondents by sampling random telephone numbers.Although interviewers currently reach about 76% of US households selected, the percentage of those contacted who agree to answer the survey has fallen. Assume that the percentage of those who agree to answer the
A soft drink company employs drivers to deliver products and stock them in grocery stores.Applicants for this position are given a preemployment test to increase the likelihood of reliability and retention. Test questions are multiple choice questions and each has five possible answers.Assume that
Stephanie is concerned about getting a job. She estimates that she has a 75% chance of getting a job offer for each job she applies for. How many jobs must she apply for to have at least a 98%chance of getting at least one offer? Create a simulation to validate your answer.
As a sales promotion, a soft drink manufacturer places winning symbols under the caps of 10% of all soft drink bottles. You buy a six-pack of soft drinks, what is the probability that you will win a prize? Create a simulation to validate your answer.
A company has 2,000 employees, 800 of whom are female; 300 of the female employees earn at least $60,000 per year and 200 of the men earn at least $60,000 per year.a. What is the probability that a randomly selected individual earns less than $60,000 per year?b. What is the probability that a
A contractor is planning a construction project to be completed in three stages. The contractor has estimated that the chance that the first stage will be completed on time is 70%. She has also estimated that if the first stage is completed on time, the chance that the second stage will be
A Company uses natural gas in its production-processing operations. Neighboring companies in its upstate New York area have successfully drilled for gas on their premises, and the company is considering following suit. Their initial expenditure would be drilling; this would cost $80,000.If they
After extensive forecasting and developing a production plan, a chocolate manufacturer knows it will need 10 tons of sugar 6 months from now. The purchasing manager has three options for acquiring the necessary sugar:a. She could buy the sugar now at the current market price and inventory it until
A car manufacturer is going to produce a new vehicle and wants to determine the amount of annual capacity it should build. The new vehicle will sell for $25,000 and have a variable cost of$19,000. Building a unit of annual capacity will cost $6000 and each unit of capacity will cost$1500 annually
A manufacturer receives regular contracts for large consignments of parts for the automobile industry. This manufacturers’ production process is such that when it is operating correctly, 90%of all parts produced meet specifications. However, the production process is prone to a particular
A contractor has decided to place a bid for a project. It is estimated that a bid of $240,000 will have a 20% chance of winning the contract; a bid of $220,000 has a 60% chance of winning, a$200,000 bid has an 80% chance of winning. It is thought that any bid under $180,000 is certain to win while
Piedmont Natural Gas (PNG) is offering a plan to cover hot water heater failures. For a customer enrolling in the plan for a year at $7.00 per month, PNG will pay up to $1000 in repairs or replacement for the customer’s hot water heater. Suppose that for the targeted customers hot water heaters
An investor is considering investing $15,000 in one of three alternatives: a certificate of deposit(CD), an Exchange Traded Fund (ETF) that is comprised of S&P 500 stocks, and a high-risk mutual fund. She considers there to be three possible outcomes: a strong, moderate, or weak stock market.
A commercial banker is considering which of two loan applications to accept. Both loans are short term (1 year) for $100,000 at an annual rate of 8.5%. With the tightening of credit, the bank is using these two customers as test cases to determine future lending practices at the bank. The first
A bank is developing policies for deciding whether to accept or deny credit card applications from existing customers. For a specific class of customers, if the bank accepts the application then there is a 95% chance the customer will remain with the bank and a 5% the customer will close
Currently a brand of cereal is contributing $1,000,000 of annual profits. The brand manager of the cereal is responsible for increasing this amount for the upcoming year and thinks the brand can do better with a “new and improved” cereal. She estimates that the annual profits for such a cereal
A real estate investor owns a small office building she has leased to a major insurance company for a rental fee based on a share of the profits. If the insurance company is successful, the present value of future rentals is estimated at $15 million. If the insurance company is not successful, the
Demand for a specific $1000 passenger cruise booking is 1000 passengers. A $50 price change results in a 10% change in demand. Fixed cost of operating the ship is $250,000 and the variable cost for a single passenger is $375. Due to the average amount of profits for a booking due to food, drinks,
Your company is bidding against three competitors to supply office furniture for a new bank headquarters. The cost to provide the furniture is estimated to be between $950,000 and$1,150,000. The company has bid against the three companies many times before. Assume triangular distributions for each
A company is bidding to provide new computers to a consulting firm. The cost to provide the computers is $650,000. The company has bid against several of the companies many times before and estimates the bids to range between $550,000 and $850,000.Assume a uniform distribution for the bids.a.
Colonial Developers is a commercial land developer that specializes in building shopping centers and wants to develop land near New Bern, North Carolina. Colonial expects that the Net Present Value (∼ profit over time in today’s dollars) without the cost of the land will be $50,000,000.In other
A local dairy manufactures ice cream as part of its operations. It supplies ice cream to 75 local restaurants. The dairy makes a 5-gal size of ice cream for these restaurants. Fifteen of these restaurants are frequent customers and order ice cream about 60% of the time (about 6 out of 10 days).
A dairy distribution center supplies 15 grocery stores with milk each week. Each week, on average, 60% of the grocery stores order a delivery of a pallet of milk containing 100 gal of milk.The milk is delivered once a week to the distribution center before orders from the grocery stores are
An online/catalog retailer will sell Adirondack chairs this season. The retailer purchases the chairs from a supplier at a cost of $175 and will sell them for $250. Demand has been forecasted to be 2000 chairs this season, but is not known for certain and could range anywhere from 1000 to 3000
You have a coin that you know is biased; one side has a higher probability of turning up than the other side. Create a simulation that shows a process by which you can use this coin to make fair decisions (decisions with equal likelihood). Pepys initially thought that outcome (c) had the highest
The Newton–Pepys problem is a probability problem concerning the probability of throwing sixes from a certain number of dice. In 1693 Samuel Pepys and Isaac Newton corresponded over a problem posed by Pepys in relation to a wager he planned to make. The problem was:Which of the following three
An investment magazine assessed the performance of 277 mutual funds over the previous 10 years. For each of the 10 years, they determined which funds performed better than the S&P 500.The research showed that 5 of the 277 funds performed better than the S&P 500 for 8 or more of the 10 years. Given
Construct a simulation to estimate the probability distribution for the number of heads when flipping 10 coins simultaneously. Show how this directly relates to Galton’s Quincunx.
An insurance company has two classes of car insurance customers. The first class has a rate of incidence of one car totaled per 100,000 customers; the second class has a rate of one car totaled per 1,000 customers. The current rate for the low-risk class for insuring a $25,000 car is $350 per year.
A cell phone manufacturer offers an extended warranty for $100 for a cell phone that costs $400.The rate of claims is approximately 1 claim per 500 warranty purchases; that is, of 500 people who buy the extended warranty only about 1 person files a claim and has the phone replaced.a. Should people,
Assume deaths from motor vehicle accidents occurred at a rate of 15.5 per 100,000 people (such information is available from the Statistical Abstract of the United States or from actuarial data).Furthermore, suppose the insurance company sells policies that offer to pay $100,000 if an insured
A FedEx contractor owns 50 trucks in a region. Ten of the trucks are relatively new and each of these trucks has a 95% chance of being in service on any day. Twenty trucks are older and only have a 90% chance of being in service on any day. Twenty trucks are much older and have a 80%chance of not
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