Operations Research An Introduction 11th Edition Hamdy A. Taha - Solutions

Consider the Q-P curve Q = 80 − 3P.(a) Determine the inelastic and elastic price ranges.(b) Given the current price is $15, calculate its point elasticity. Should the price be increased or decreased to increase the revenue. Explain why?(c) Repeat assuming the current price is $10.
A professor of political science wants to predict the outcome of a school board election. Three candidates, Ivy (I), Bahrn (B), and Smith (S), are running for one position. There are three categories of voters: left (L), center (C), and right (R). The candidates are judged based on three factors:
The following table provides a 14-day record of weather conditions and whether or not golf was played on each day.(a) Compute the associated training set.(b) Determine the decision whether or not golf should be played tomorrow for the given weather forecast.(c) Compute the posterior probabilities
You have been invited to play the Fortune Wheel game on television. The wheel operates electronically with two buttons that produce hard (H) or soft (S) spin. The wheel itself is divided into white (W) and red (R) half-circle regions. You have been told that the wheel is designed to stop on white
A retailer receives 75% of its batteries from Factory A and 25% from Factory B. The percentages of defectives produced by A and B are known to be 1% and 2%, respectively.A customer has just bought a battery randomly from the retailer.(a) What is the probability that the battery is defective?(b) If
A retailer replenishes one of its products from four factories, A, B, C, and D: A provides 20% of the supply, B supplies 25%, C’s share is 32%, the rest comes from D. The percentages of defectives from the four factories are 1, 2, 1.5, and 2.8, respectively, includes 10% defective items, whereas
Statistics show that 70% of all men have some form of prostate cancer. The PSA test will show positive 90% of the time for afflicted men and 10% of the time for healthy men. What is the probability that a man who tested positive does have prostate cancer?
Imagine a hypothetical country of 100 million ruled by a ruthless dictator bent on suppressing opposition. The opposition is estimated at 1000 individuals, all living in exile. The dictatorship is using a highly sophisticated voice-recognition wiretapping system that will alert the country’s
You have the chance to invest in three mutual funds: utility, aggressive growth, and global. The value of your investment will change depending on the market conditions. There is a 10% chance the market will go down, 50% chance it will remain moderate, and 40% chance it will perform well. The
TriStar plans to open a new plant in Arkansas. The company can open a full-size plant now or a small-size plant that can be expanded 2 years later if warranted by high demand. The time horizon for the decision problem is 10 years. TriStar estimates that the probabilities for high and low demands
Farmer McCoy can plant either corn or soybeans. The probabilities that the next harvest prices will go up, stay the same, or go down are .25, .30, and .45, respectively. If the prices go up, the corn crop will net $30,000 and the soybeans will net $10,000. If the prices remain unchanged, McCoy will
An automatic machine produces α (thousands of) units of a product per day. As α increases, the proportion of defectives, p, goes up according to the following probability density functionEach defective item incurs a loss of $50. A good item yields $5 profit.(a) Develop a decision tree for this
Acme Manufacturing uses a chemical in one of its processes. The shelf life is 1 month, and any amount left is destroyed. The amount, x, in gallons of the chemical used by Acme is represented by the following distribution:The actual consumption of the chemical occurs instantaneously at the start of
You have the chance to invest your money in either a 7.5% bond that sells at face value or an aggressive growth stock that pays only 1% dividend. If inflation occurs, the interest rate will go up to 8%, in which case the principal value of the bond will go down by 10%, and the stock value will go
AFC is about to launch its new Wings ‘N Things fast food nationally. The research department is convinced that Wings ‘N Things will be a great success and wants to introduce it immediately in all AFC outlets without advertising. The marketing department sees “things” differently and wants
A manufacturer has used linear programming to determine the optimum production mix of the various TV models it produces. Recent information received by the manufacturer indicates that there is a 40% chance that the supplier of a component used in one of the models may raise the price by $35. The
A fair coin is flipped three successive times. You receive $1.00 for each head (H) that turns up and an additional $.25 for each two successive heads that appear (remember that HHH includes two sets of HH). However, you give back $1.10 for each tail that shows up. You have the options to either
The outer diameter, d, of a cylinder is processed on an automatic machine with upper and lower tolerance limits of d + tU and d − tL. The production process follows a normal distribution with mean μ and standard deviation σ. Oversized cylinders are reworked at the cost of c1 dollars each.
Cohan and Associates (1984). Modern forest management uses controlled fires to reduce fire hazards and to stimulate new forest growth. Management has the option to postpone or plan a burning. In a specific forest tract, if burning is postponed, a general administrative cost of $300 is incurred. If
Historical data at Acme Manufacturing estimate a 5% chance that a batch of widgets will be unacceptable (bad). A bad batch has 15% defective items, and a good batch includes only 4% defective items. Letting a = θ1 and a = θ2 represent a good and a bad batch, respectively, the associated prior
An investment of $10,000 in a high-risk venture has a 50-50 chance over the next year of increasing to $14,000 or decreasing to $8000. Thus the net return can be either $4000 or −$2000.(a) Assuming a risk-neutral investor and a utility scale from 0 to 100, determine the utility of $0 net return
Data in a community college show that 75% of new students who took calculus in high school do well, compared with 50% of those who did not take calculus. Admissions for the current academic year show that only 30% of the new students have completed a course in calculus. What is the probability that
Elektra receives 75% of its electronic components from vendor A and the remaining 25% from vendor B. The percentage of defectives from vendors A and B are 1% and 2%, respectively. When a random sample of size 5 from a received lot is inspected, only one defective unit is found. Determine the
You are the author of what promises to be a successful novel. You have the option to either publish the novel yourself or through a publisher. The publisher is offering you $20,000 for signing the contract. If the novel is successful, it will sell 200,000 copies. Else, it will sell 10,000 copies
Hank is an intelligent student and usually makes good grades, provided that he can review the course material the night before the test. For tomorrow’s test, Hank is faced with a small problem: His fraternity brothers are having an all-night party in which he would like to participate. Hank has
You are a student at the University of Arkansas and desperately want to attend the next Razorbacks basketball game. The problem is that the admission ticket costs $10, and you have only $5. You can bet your $5 in a poker game, with a 50-50 chance of either doubling your money or losing all of
The Golden family has just moved to a location where earthquakes are not uncommon. They must decide whether to build their house according to the high-standard earthquake code. The construction cost using the earthquake code is $850,000; otherwise, a comparable house can be constructed for only
For the upcoming planting season, Farmer McCoy can plant corn (a1), wheat (a2), or soybeans (a3) or use the land for grazing (a4). The payoffs associated with the different actions are influenced by the amount of rain: heavy rainfall (s1), moderate rainfall (s2), light rainfall (s3), or drought (s4
In games (a) and (b) given below, the payoff is for player A. Each game has a pure strategy solution. In each case, determine the strategies that define the saddle point and the value of the game.(a)(b) A₁ A₂ A3 B₁ 8 B2 7 6 8 9 5 B3 2 4 B4 8 5 3 5
In games (a) and (b) below, the payoff is for player A. Determine the values of p and q that will make (A2 , B2) a saddle point:(a)(b) A₁ A₂ A3 B₁ 1 P 6 B₂ 9 5 2 B3 6 10 3
Let aij be the (i, j)th element of a payoff matrix with m strategies for player A and n strategies for player B. The payoff is for player A. Prove that max min a ≤min max ai i j j i
In the games below, the payoff is for player A. Specify the range for the value of the game in each case.(a)(b)(c)(d) B₁ A₁ 1 A2 A3 A4 B₂ B 3 9 6 2 3 -5 7 -2 4 B₁ 0 8 4 10 -3 -2 -5
Robin travels between two cities and may use one of two routes: Route A is a fast four-lane highway, and route B is a long winding road. She has the habit of driving “ superfast.” The highway patrol has a limited police force. If the full force is allocated to the route driven by Robin, she is
Two companies promote two competing products. Currently, each product controls 50% of the market. Because of recent improvements in the two products, each company plans to launch an advertising campaign. If neither company advertises, equal market shares will continue. If either company launches a
Solve the following games graphically. The payoff is for Player A.(a)(b) A₁ A2 B1 1 2 B2 -3 4 B3 7 -6
Consider the following two-person, zero-sum game:(a) Verify that the strategiesfor B are optimal, and determine the value of the game.(b) Show that the optimal value of the game equals B₁ B₂ B3 A₁ 5 50 50 A₂ 1 A3 10 1.1 1 10
UA and DU are devising their strategies for the 1994 national championship men’s college basketball game. Assessing the strengths of their respective “benches,” each coach comes up with four strategies for rotating the players during the game. The ability of each team to score 2-pointers,
On a picnic outing, 2 two-person teams are playing hide-and-seek. There are four hiding locations (A, B, C, and D), and the two members of the hiding team can hide separately in any two of the four locations. The other team can then search any two locations. The searching team gets a bonus point if
Colonel Blotto’s army is fighting for the control of two strategic locations. Blotto has two regiments and the enemy has three. A location will fall to the army with more regiments. Otherwise, the result of the battle is a draw.(a) Formulate the problem as a two-person zero-sum game, and solve by

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