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practical management science

Practical Management Science, Revised 3rd Edition Wayne L Winston, S. Christian Albright - Solutions

Describe what happens to the optimal shipping plan at this point.
Use SolverTable appropriately to do the following. Decrease the unit shipping costs from plants and warehouses to customer 1, all by the same amount, until it is no longer optimal for customer 1 to ship to customer
In the original RedBrand problem, the costs for shipping from plants or warehouses to customer 2 were purposely made high so that it would be optimal to ship to customer 1 and then let customer 1 ship to customer
In the original RedBrand problem, suppose the plants cannot ship to each other and the customers cannot ship to each other. Modify the model appropriately and reoptimize. How much does the total cost increase because of these disallowed routes?
After giving this further thought, we deleted this constraint as being redundant. Why could we do this? Specifically, why can’t one or more of the flows found by Solver be greater than 1? (Hint:Think in terms of flows out of and into the nodes in the network diagram.)
When we (the authors) originally developed the bus route assignment model, we included an arc capacity constraint: Flow
In the optimal solution to the machine-to-job assignment problem, jobs 3 and 4 are assigned to different machines. Suppose we impose the restriction that these jobs must be assigned to the same machine.Change the model to accommodate this restriction and find the new optimal solution.
Suppose we impose the restriction that jobs 1 and 2 must be assigned to different machines. Change the model to accommodate this restriction and find the new optimal solution.
In the optimal solution to the machine-to-job assignment problem, jobs 1 and 2 are both assigned to machine
We modeled the bus route assignment problem with the alternative form of the transportation model (as in Figure 5.7). Model it instead with the “standard” form(as in Figure 5.2). Discuss the pros and cons of these two approaches for this particular example.Skill-Extending Problems
If you could increase one of these capacities by 1, which would you increase? Why?
In the machine-to-job assignment problem, the current capacities of the machines are 1, 2, 1, 2, and
Modify the original Grand Prix example as follows.Increase the demands at the regions by 200 each, so that total demand is well above total plant capacity.This means that some demands cannot be supplied.Suppose there is a unit “penalty” cost at each region for not supplying an automobile. Let
Modify the original Grand Prix example as follows.Increase the demands at the regions by 200 each, so that total demand is well above total plant capacity.However, now interpret these “demands” as “maximum sales,” the most each region can accommodate, and change the “demand” constraints
Continuing the previous problem (with capacity 300 at plant 2), suppose we want to see how much extra capacity and extra demand we can add to plant 1 and region 2 (the same amount to each) before the total shipping cost stops decreasing and starts increasing.Use SolverTable appropriately to find
Then the total capacity is equal to the total demand. Reoptimize the model. You should find that the optimal solution uses all capacity and exactly meets all demands with a total cost of $176,050. Now increase the capacity of plant 1 and the demand at region 2 by 1 automobile each, and optimize
Here is a problem to challenge your intuition. In the original Grand Prix example, reduce the capacity of plant 2 to
In the Grand Prix example with varying tax rates, the optimal solution uses all available plant capacity and more than satisfies customer demands. Will this always be the case? Experiment with the unit selling prices and/or tax rates to see whether the company ever uses less than its total
Modify the model and find the optimal solution. How does it differ from the solution without upper limits?
In the Grand Prix example with varying tax rates, the optimal solution more than satisfies customer demands.Modify the model so that regions have not only lower limits on the amounts they require, but upper limits on the amounts they can sell. Assume these upper limits are 50 autos above the
Suppose in the original Grand Prix example that the routes from plant 2 to region 1 and from plant 3 to region 3 are not allowed. (Perhaps there are no railroad lines for these routes.) How would you modify the original model (Figure 5.2) to rule out these routes? How would you modify the
Discuss how Keefer might use a blending model to maximize its profit.
Keefer Paper produces recycled paper from paper purchased from local offices and universities. The company sells three grades of paper: high-brightness paper, medium-brightness paper, and low-brightness paper. The high-brightness paper must have a brightness level of at least 90, the
It is February 15, 2006. Three bonds, as listed in the file P04_128.xlsx, are for sale. Each bond has a face value of $100. Every 6 months, starting 6 months from the current date and ending at the expiration date, each bond pays 0.5*(coupon rate)*(Face value).At the expiration date the face value
At the beginning of month 1, GE Capital has 50 million accounts. Of these, 40 million are paid up (0-due), 4 million are 1 month overdue (1-due), 4 million are 2 months overdue (2-due), and 2 million are 3 months overdue (3-due). After an account is more than 3 months overdue, it’s written off as
During each 6-hour period of the day, the Bloomington Police Department needs at least the number of police officers shown in the file P04_125.xlsx. Police officers can be hired to work either 12 consecutive hours or 18 consecutive hours. Police officers are paid$4 per hour for each of the first 12
Based on Robichek et al. (1965). At the beginning of month 1, Finco has $400 in cash. At the beginning of months 1, 2, 3, and 4, Finco receives certain revenues, after which it pays bills. (See the file P04_124.xlsx.) Any money left over can be invested for 1 month at the interest rate of 0.1% per
Group 1 has 1000 members, and group 2 has 1500 members.Chandler wants to set prices for each product to ensure that group 1 members purchase product A and group 2 members purchase product B. Determine how Chandler can maximize its revenue.
Here, the“premium” of a product is its value minus its price.Similarly, a customer is willing to buy B if she believes the Premium of product B is greater than or equal to the Premium of product A and the Premium of product B is greater than or equal to
The values each customer places on a unit of A and B are shown in the file P04_123.xlsx. Each customer will buy either product A or product B, but not both. A customer is willing to buy product A if she believes that the Premium of product A is greater than or equal to the Premium of product B and
Based on Dobson and Kalish (1988). Chandler Enterprises produces two competing products, A and B. The company wants to sell these products to two groups of customers, group 1 and group
Based on Franklin and Koenigsberg (1973). The city of Busville contains three school districts. The numbers of minority and nonminority students in each district are given in the file P04_121.xlsx. The local court has decided that each of the town’s two high schools (Cooley High and Walt Whitman
Determine how to maximize Bexter’s profit.
The average quality level of the units sold must be at least
Each processed unit of raw material 1 yields 2 units of A and 3 units of B. It costs $3 to purchase and process a unit of raw material 2.Each processed unit of raw material 2 yields 1 unit of A and 2 units of B. The unit prices for the products are A, $5; B, $4; C, $25. The quality levels of each
It costs $6 to purchase and process 1 unit of raw material
Bexter Labs produces three products: A, B, and C.Bexter can sell up to 30 units of product A, up to 20 units of product B, and up to 20 units of product C.Each unit of product C uses 2 units of A and 3 units of B and incurs $5 in processing costs. Products A and B are produced from either raw
Each process 2 run yields 1 ounce of product B and 0.8 ounce of liquid waste. Process 2 incurs $8 in costs. Chemco can dispose of liquid waste in the Port Charles River or use the waste to produce product C or product D. Government regulations limit the amount of waste Chemco is allowed to dump
Each time process 1 is run, 1 ounce of productAand 1 ounce of liquid waste are produced. Each time process 2 is run requires 3 hours of processing time, 2 ounces of input 2, and 1 ounce of input
It costs $1 to run process
Each pound of raw material can yield 2 ounces of input 1, requiring 2 hours of processing time and incurring $2 in processing costs.Each pound of raw material can yield 3 ounces of input 2, requiring 2 hours of processing time and incurring $4 in processing costs. Two production processes are
Each week, Chemco can purchase unlimited quantities of raw material at $6 per pound. Each pound of purchased raw material can be used to produce either input 1 or input
Each unit of product 2 can be sold or processed further. Each unit of product 2 that is processed further yields 0.8 unit of product 5 and 0.3 unit of product 6.Up to 1000 units of product 5 can be sold, and up to 800 units of product 6 can be sold. Up to 3000 units of raw material can be purchased
Up to 1200 units of product 1 can be sold, and up to 300 units of product 2 can be sold. Demand for products 3 and 4 is unlimited. Each unit of product 1 can be sold or processed further. Each unit of product 1 that is processed further yields 1 unit of product
Flexco produces six products in the following manner.Each unit of raw material purchased yields 4 units of product 1, 2 units of product 2, and 1 unit of product
Each month, 4000 barrels of crude 1, at $45 per barrel, and 7000 barrels of crude 2, at$55 per barrel, can be purchased. All gas produced can be sold at the following per-barrel prices: gas 1,$85; gas 2, $90; gas 3, $95. Determine how to maximize Sunco’s profit (revenues less costs). Assume that
Running process 3 for an hour costs $14 and requires 2 barrels of crude 2 and 3 barrels of gas 2.The output from running process 3 for an hour is 2 barrels of gas
The output from running process 2 for an hour is 3 barrels of gas
The output from running process 1 for an hour is 2 barrels of gas 1 and 1 barrel of gas 2.Running process 2 for an hour costs $30 and requires 1 barrel of crude 1 and 3 barrels of crude
Sunco Oil has three different processes that can be used to manufacture various types of gasoline. Each process involves blending oils in the company’s catalytic cracker. Running process 1 for an hour costs$20 and requires 2 barrels of crude oil 1 and 3 barrels of crude oil
Assume the perton cost of holding either product in inventory for 1 month is $5.a. Determine a minimum cost production schedule for the next 4 months.b. There is an important aspect of this situation that cannot be modeled by linear programming. What is it? (Hint: If Owens makes product 1 and
A cost of $2000 is incurred each time a new machine is purchased, and a cost of $1000 is incurred if a machine is retired from service. At the end of each month, Owens would like to have at least 50 tons of each product in inventory.At the beginning of month 1, Owens has 5 machines on line 1 and 8
Owens-Wheat uses 2 production lines to produce 3 types of fiberglass mat. The demand requirements(in tons) for each of the next 4 months are shown in the file P04_115.xlsx. If it were dedicated entirely to the production of one product, a line 1 machine could produce either 20 tons of type 1 mat or
Each hour from 10 A.M. to 7 P.M., Bank One receives checks and must process them. Its goal is to process all checks the same day they are received. The bank has 13 check processing machines, each of which can process up to 500 checks per hour. It takes one worker to operate each machine. Bank One
Mackk Engine produces diesel trucks. New government emission standards have dictated that the average pollution emissions of all trucks produced in the next 3 years cannot exceed 10 grams per truck.Mackk produces 2 types of trucks. Each type 1 truck sells for $20,000, costs $15,000 to manufacture,
Based on Robichek et al. (1965). The Korvair Department Store has $100,000 in available cash. At the beginning of each of the next 6 months, Korvair will receive revenues and pay bills as listed in the file P04_112.xlsx. It is clear that Korvair will have a short-term cash flow problem until the
The production line employees at Grummins Engine work 4 days a week, 10 hours a day. Each day of the week, the following minimum numbers of line employees are needed: Monday through Friday, 70 employees; Saturday and Sunday, 30 employees.Grummins employs 110 line employees. Determine how to
The Wild Turkey Company produces two types of turkey cutlets for sale to fast-food restaurants. Each type of cutlet consists of white meat and dark meat.Cutlet 1 sells for $4 per pound and must consist of at least 70% white meat. Cutlet 2 sells for $3 per pound and must consist of at least 60%
Silvco has sufficient furnace capacity to melt or refire germanium for at most 20,000 transistors per month. Silvco’s monthly demands are for 1000 grade 4 transistors, 2000 grade 3 transistors, 3000 grade 2 transistors, and 3000 grade 1 transistors. Determine how to minimize the cost of producing
Based on Smith (1965). Silicon Valley Corporation(Silvco) manufactures transistors. An important aspect of the manufacture of transistors is the melting of the element germanium (a major component of a transistor) in a furnace. Unfortunately, the melting process yields germanium of highly variable
Incineration reduces each ton of waste to 0.2 ton of debris, which must be dumped at one of two landfills. Each landfill can receive at most 200 tons of debris per day. It costs$3 per mile to transport a ton of material (either debris or waste). Distances (in miles) between locations are listed in
City 1 produces 500 tons of waste per day, and city 2 produces 400 tons of waste per day. Waste must be incinerated at incinerator 1 or 2, and each incinerator can process up to 500 tons of waste per day. The cost to incinerate waste is $40 per ton at incinerator 1 and$30 per ton at incinerator
Based on Charnes and Cooper (1955). Alex Cornby makes his living buying and selling corn. On January 1, he has 500 tons of corn and $10,000. On the first day of each month, Alex can buy corn at the following prices per ton: January, $300; February, $350;March, $400; April, $500. On the last day of
The police department wants to schedule police officers to minimize the number whose days off are not consecutive. Determine how to accomplish this goal.
Based on Rothstein (1973). The Springfield City Police Department employs 30 police officers. Each officer works 5 days per week. The crime rate fluctuates with the day of the week, so the number of police officers required each day depends on the day of the week, as follows: Saturday, 28; Sunday,
Gotham City National Bank is open Monday through Friday from 9 A.M. to 5 P.M. From past experience, the bank knows that it needs the numbers of tellers listed in the file P04_104.xlsx. Gotham City Bank hires two types of tellers. Full-time tellers work 9 A.M. to 5 P.M. five days a week, with one
Air conditioners can be produced in either New York or Los Angeles.It takes 1.5 hours of skilled labor to produce an air conditioner in Los Angeles, and it takes 2 hours in New York. It costs $400 to produce an air conditioner in Los Angeles, and it costs $350 in New York.During each month, each
During the next 3 months, Airco must meet (on time)the following demands for air conditioners: month 1, 300; month 2, 400; month 3,
Determine how Eastinghouse can maximize its daily profit.
Each day, Eastinghouse produces capacitors during three shifts: 8 A.M. to 4 P.M., 4 P.M. to 12 A.M., and 12 A.M. to 8 A.M. The hourly salary paid to the employees on each shift, the price charged for each capacitor made during each shift, and the number of defects in each capacitor produced during
Aluminaca produces 100-foot-long, 200-foot-long, and 300-foot-long ingots for customers. This week’s demand for ingots is listed in the file P04_101.xlsx.Aluminaca has four furnaces in which ingots can be produced. During 1 week, each furnace can be operated for 50 hours. Because ingots are
Help the client solve her problem.After you have solved this problem, give an intuitive explanation of the solution found by Solver.
Then her Saks balance at the beginning of month 2 is $20,000 [$5000 0.005(20,000)]. This follows because she incurs 0.005(20,000) in interest charges on her Saks card during month
You are a CFA (chartered financial analyst). An overextended client has come to you because she needs help paying off her credit card bills. She owes the amounts on her credit cards listed in the file P04_100.xlsx. The client is willing to allocate up to$5000 per month to pay off these credit
The ZapCon Company is considering investing in three projects. If it fully invests in a project, the realized cash flows (in millions of dollars) will be as listed in the file P04_99.xlsx. For example, project 1 requires a cash outflow of $3 million today and returns$5.5 million 3 years from now.
Pear produces low-budget cars. Each car is sold for$7900. The raw material in a car costs $5000. Labor time and robot time are needed to produce cars. A worker can do the needed labor on, at most, 100 cars per month; a robot can complete the needed work on, at most, 200 cars per month. Initially,
Broker Sonya Wong is currently trying to maximize her profit in the bond market. Four bonds are available for purchase and sale at the bid and ask prices shown in the file P04_97.xlsx. Sonya can buy up to 1000 units of each bond at the ask price or sell up to 1000 units of each bond at the bid
Carco has a $1,500,000 advertising budget. To increase its automobile sales, the firm is considering advertising in newspapers and on television. The more Carco uses a particular medium, the less effective each additional ad is. The file P04_96.xlsx lists the number of new customers reached by each
Determine how to maximize Bexter’s profit.
The average quality level of the units sold must be at least
Each processed unit of raw material 2 yields 1 unit of A and 2 units of B. The unit prices for the products are A, $5; B, $4; C, $25. The quality levels of each product are: A, 8; B, 7; C,
Each processed unit of raw material 1 yields 2 units of A and 3 units of B. It costs $3 to purchase and process a unit of raw material
It costs $6 to purchase and process 1 unit of raw material
Bexter Labs produces three products: A, B, and C.Bexter can sell up to 3000 units of product A, up to 2000 units of product B, and up to 2000 units of product C. Each unit of product C uses 2 units of A and 3 units of B and incurs $5 in processing costs. Products A and B are produced from either
Molecular Products produces 3 chemicals: B, C, and D. The company begins by purchasing chemical A for a cost of $6 per 100 liters. For an additional cost of $3 and the use of 3 hours of skilled labor, 100 liters of A can be transformed into 40 liters of C and 60 liters of B. Chemical C can either
A total of 120 hours of skilled labor and 100 ounces of raw material are available. Determine how to maximize Capsule’s sales revenues.
Drug 1 sells for $6 per ounce, and drug 2 sells for$4 per ounce. Chemicals 1 and 2 can be produced by one of two production processes. Running process 1 for an hour requires 7 ounces of raw material and 2 hours skilled labor, and it yields 3 ounces of each chemical. Running process 2 for an hour
By weight, drug 1 must contain at least 65% chemical 1, and drug 2 must contain at least 55% chemical
The drugs are produced by blending two chemicals: 1 and
Capsule Drugs manufactures two drugs: 1 and
You can calculate the risk index of an investment by taking the absolute values of percentage changes in the value of the investment for each year and averaging them. Suppose you are trying to determine what percentage of your money you should invest in T-bills, gold, and stocks. The file
You own a wheat warehouse with a capacity of 20,000 bushels. At the beginning of month 1, you have 6000 bushels of wheat. Each month, wheat can be bought and sold at the prices per 1000 bushels listed in the file P04_89.xlsx. The sequence of events during each month is as follows:■ You observe
The Internal Revenue Service (IRS) has determined that during each of the next 12 months it will need the numbers of supercomputers given in the file P04_88.xlsx. To meet these requirements, the IRS rents supercomputers for a period of 1, 2, or 3 months.It costs $1000 to rent a supercomputer for 1
At the beginning of quarter 1, there are 300 autos in stock. The company has the capacity to produce at most 3000 cars per quarter.At the beginning of each quarter, the company can change production capacity. It costs $100 to increase quarterly production capacity by one unit. For example, it would
During the next 4 quarters, Dorian Auto must meet(on time) the following demands for cars: 4000 in quarter 1; 2000 in quarter 2; 5000 in quarter 3;1000 in quarter
If you did not include the over and under changing cells, why would your model fail to be linear?]
Based on Charnes and Cooper (1955). A small company is trying to determine employee salary based on following attributes: effectiveness, responsibility, initiative, experience, education, self expression, planning ability, intelligence, and the ability to get things done. Each of the company’s
What is the minimum number of trainees that need to be hired during months 1 to 8? (Note: Trainees must be integers. Experienced workers will probably end up being fractional, but don’t worry about this.)
AdminaStar processes Medicare claims. At the beginning of month 1 they have a backlog of 40,000 difficult claims and 60,000 easy claims. The predicted claim volume for months 1 through 8 is listed in the file P04_85.xlsx. At the beginning of month 1, AdminaStar has 70 experienced claim processors.
For annual interest rates of 10%, 11%, 12%, 13%, and 14%, use Solver to find the amount of each year’s monthly payment.

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