Concept explainers
a)
To determine: The way to minimize the bus company’s costs over the period of next five years.
Linear programming:
It is a mathematical modeling procedure where a linear function is maximized or minimized subject to certain constraints. This method is widely useful in making a quantitative analysis which is essential for making important business decisions.
a)
Explanation of Solution
Model:
Solver input:
The solver input is selected from under the “Data” tab in Excel and the input is given as shown below:
Formula:
The total cost is $3,420,000.
b)
To use: The solver table to determine the .change in the total number of hired, fired, total cost change due to the change in unit hiring, firing where each of them increases by the same percentage.
Linear programming:
It is a mathematical modeling procedure where a linear function is maximized or minimized subject to certain constraints. This method is widely useful in making a quantitative analysis which is essential for making important business decisions.
b)
Explanation of Solution
One-way solver table:
The one-way solver table is selected and the input is given as shown below:
Output:
In the given range of percent increases, the total of hired and fired does not change. But, the cost increases.
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Chapter 4 Solutions
Practical Management Science
- An experiment that involves learning in animals requires placing white mice and rabbits into separate, controlled environments: environment I and environment II. The maximum amount of time available in environment I is 420 minutes, and the maximum amount of time available in environment II is 624 minutes. The white mice must spend 10 minutes in environment I and 24 minutes in environment II, and the rabbits must spend 12 minutes in environment I and 16 minutes in environment II. (a) Write a system of inequalities that describes the constraints on the number of each type of animal used in the experiment. (Let x represent the number of mice, and let y represent the number of rabbits.) environment I time constraint environment II time constraint x ≥ 0 experiment constraint, mice y ≥ 0 experiment constraint, rabbits (b) Graph the solution of the system of inequalities and find the corners of the solution region.arrow_forwardFRUIT COMPUTER COMPANY Fruit Computer Company manufactures memory chips in batches of ten chips. From past experience, Fruit knows that 80% of all batches contain 10% (1 out of 10) defective chips, and 20% of all batches contain 50% (5 out of 10) defective chips. If a good (that is, 10% defective) batch of chips is sent to the next stage of production, processing costs of $4000 are incurred, and if a bad batch (50% defective) is sent on to the next stage of production, processing costs of $16000 are incurred. Fruit also has the alternative of reworking a batch at a cost of $4000. A reworked batch is sure to be a good batch. Alternatively, for a cost of $400, Fruit can test one chip from each batch in an attempt to determine whether the batch is defective. QUESTIONS 1.Determine a strategy so Fruit can minimize the expected total cost per batch. 2.Compute the EVSI and EVPI.arrow_forwardA political party is planning a ninety-minute television show. The show will have at least 9 minutes of direct requests for money from viewers. Three of the party's politicians will be on the show- a senator, a congresswoman, and a governor. The senator, a party "elder statesman," demands that he be on screen for at least twice as long as the governor. The total time taken by the senator and the governor must be at least twice the time taken by the congresswoman. Based on a pre-show survey, it is believed that 37, 41, and 45 (in thousands) viewers will watch the program for each minute the senator, congresswoman, and governor, respectively, are on the air. Find the time that should be allotted to each politician in order to get the maximum number of viewers. Find the maximum number of viewers. The quantity to be maximized, z, is the number of viewers in thousands. Let x, be the total number of minutes allotted to the senator, × be the total number of minutes allotted to the…arrow_forward
- Apply Linear Programming to the Folling Question: Dan Reid, chief engineer at New Hampshire Chemical, Inc., has to decide whether to build a new state-of-art processing facility. If the new facility works, the company could realize a profit of $200,000. If it fails, New Hampshire Chemical could lose $150,000. At this time, Reid estimates a 60% chance that the new process will fail. The other option is to build a pilot plant and then decide whether to build a complete facility. The pilot plant would cost $10,000 to build. Reid estimates a fifty-fifty chance that the pilot plant will work. If the pilot plant works, there is a 90% probability that the complete plant, if it is built, will also work. If the pilot plant does not work, there is only a 20% chance that the complete project (if it is constructed) will work. Reid faces a dilemma. Should he build the plant? Should he build the pilot project and then make a decision? Help Reid by analyzing this problemarrow_forwardA college student works in both the school cafeteria and library. She works no more than 12 hours per week at the cafeteria, and no more than 16 hours per week at the library. She must work at least 20 hours each week. Write a system of inequalities that describes all the given conditions. Write a system of inequalities letting x= number of hours worked at the cafeteria per week and y = number of hours worked at the library per week. x+yz x≤ ysarrow_forwardA catering company must have the following number of clean napkins available at the beginning of each of the next four days: day 1: 15, day 2: 12, day 3: 18, and day 4: 6. After being used, a napkin can be cleaned by one of two methods: fast service or slow service. Fast service costs $0.10 per napkin, and a napkin cleaned via fast service is available for use the day after it is last used. Slow service costs $0.06 per napkin, and a napkin cleaned via slow service is available two days after they were last used. New napkins can be purchased for a cost of $0.20 per napkin. Part A: Formulate the problem as a minimum cost transportation problem.arrow_forward
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- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,