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Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 26EQ

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Laura's yard is in the shape of a square and a half-circle.
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What is the approximate area of Laura's yard?
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D) 743 m²
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Recreate the given figure for a call center that wants to achieve a 40 percent no hold rate. Suppose that agents only become cost effective (where the revenue they generate exceeds their cost) if they have 90 percent utilization. How large, in terms of number of agents, does the call center need to be to have agents that are generating a positive profit? If mean call time is 5 minutes, what would the arrival rate need to be for 90 percent agent utilization with this many agents?
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Workers at a particular mining site receive an average of 35 days paid vacation, which is lower than the national average. The manager of this plant is under pressure from a local union to increase the amount of paid time off. However, he does not want to give more days off to the workers because that would be costly. Instead he decides he should fire 10 employees in such a way as to raise the average number of days off that are reported by his employees. In order to achieve this goal, should he fire employees who have the most number of days off, least number of days off, or those who have about the average number of days off? a. He should fire employees who have the most number of days off. b. No matter who he fires, it will not increase the amount of paid time off. c. He should fire employees who have the average number of days off. d. He should fire employees who have the least number of days off.
A food manufacturing company wants to hire an auditing firm to asses their food safety performance. Two auditing firms are considered: firm A will change 42$/hr and a flat fee of $4500, while firm B will charge 50$/hr with a flat fee of $3900. What is the break-even point in number of required auditing hours that would yield equal value from both companies?
Consider the example of the three-step airport security. The first step, verifying ID andboarding pass, takes 30 seconds per passenger. The second step, searching the passengerfor metal objects using a metal detector, takes 10 seconds per passenger. The third step,running the carry-on luggage through an X-ray machine, takes 60 seconds per passenger. Assume that there are many customers waiting in the process and that each of thethree employees gets paid $15 per hour.(a) What is the cost of direct labor?(b) What is the labor content?(c) What is the average labor utilization?
Consider the market depicted in the graph and assume the government imposes a price floor of P2. At P2, 150 units of the good are supplied (wish to be sold) and 50 units of the good are demanded (wish to be bought). Choose the correct ones: Without an enforcement mechanism, the effect of a binding price floor will be negligible because it will simply be ignored because buyers and sellers enrich themselves by trading below the floor price. With an enforcement mechanism, the effect of a binding price floor may still be negligible if the enforcement mechanism is easy to evade or doesn't impose a significant penalty for selling below the price floor. Without an enforcement mechanism, the effect of a binding price floor will be negligible because it will simply be ignored because buyers and sellers enrich themselves by trading above the floor price. With an enforcement mechanism, the effect of a binding price floor may still be negligible if the enforcement mechanism is easy to evade or…

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