Questions and Answers of Operations Research An Introduction

The use of price differentiation to increase revenue in airlines need not be limited to two-segmentation fare classes only (as evident by the seemingly run-out-of-alphabet letters used presently by
Consider the hypothetical Q-P demand curve of Problem 14-3, Q = 100 / P . The revenue at any point is R = PQ at any point (Q-P) is the same and equals 100. Show that the four-fare Q-segmentation (0,
Prove that unit elasticity satisfies the necessary condition for determining the maximum revenue.
Categorize the demand for each of the following goods as likely elastic or likely inelastic: Gasoline, soft drinks, cars, medication, computers, home utilities (water, electric, and gas), air travel,
The daily number of meals, Q, in a popular 24-hour fast food restaurant is estimated as a function of the price per meal by the demand curve Q = 5000 − 250P.(a) The restaurant currently charges
Consider the two-hierarchal data of Problem 15-1. Copy the weights in a logical order into the solution summary section of the spreadsheet excelAHP.xls, then develop the formula for evaluating the
The personnel department at C&H has narrowed the search for a new hire to three candidates: Steve (S), Jane (J), and Maisa (M). The final selection is based on three criteria: personal interview
Kevin and June Park (K and J) are in the process of buying a new house. Three houses, A, B, and C, are available. The Parks have agreed on two criteria for the selection of the house—amount of yard
An individual is in the process of buying a car and has narrowed the choices to three models: M1, M2, and M3. The deciding factors include purchase price (PP), maintenance cost (MC), cost of city
A new author sets three criteria for selecting a publisher for an OR textbook: royalty percentage (R), marketing (M), and advance payment (A). Two publishers, H and P, have expressed interest in the
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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%
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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

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