Questions and Answers of Operations Research An Introduction

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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