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
- A 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_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 S0.20 per napkin. Part A: Formulate the problem as a minimum cost transportation problem. Part B: Solve the problem (provide exact values for all variables and the optimal objective function).arrow_forwardA trust officer at the Blacksburg National Bank needs to determine how to invest $150,000 in the following collection of bonds to maximize the annual return. Bond Annual Return Maturity Risk Tax Free A 9.5% Long High Yes B 8.0% Short Low Yes C 9.0% Long Low No D 9.0% Long High Yes E 9.0% Short High No The officer wants to invest at least 40% of the money in short-term issues and no more than 20% in high-risk issues. At least 25% of the funds should go in tax-free investments, and at least 45% of the total annual return should be tax free. Formulate the LP model for this problem. Create the spreadsheet model and use Solver to solve the problem. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.arrow_forward
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- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,