Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Chapter 4.3, Problem 9P
a)
Summary Introduction
To modify: The model to minimize the company’s weekly labor costs.
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)
Summary Introduction
To use: The Solver table to analyze how an alteration in the part-time labor limitation impacts the optimal solution.
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A hospital emergency room requires different numbers of nurses on different days of the week. The number of full-time employees required to be working (i.e. not on call) each day is given in the table below.
Mon
Tue
Wed
Thu
Fri
Sat
Sun
18
15
12
13
20
28
22
Hospital rules require that nurses work four consecutive days, are on call for one day, and then receive two days off. The hospital wants to meet its daily requirements, while minimizing the number of nurses that must be on staff.
A. How many total nurses are needed to be on staff for the optimal solution?
B.Suppose the hospital is experiencing a budget crunch and needs to use the nurses' on call day to temporarily staff the emergency room.
How many nurses work on Thursday in the optimal solution?
C. Suppose the hospital has 40 nurses and is not allowed to hire or fire any employees, and cannot temporarily schedule nurses on their on call days. Determine a schedule that meets the daily requirements while maximizing the number…
11. The shadow price is calculated to be 5 for a less than or equal to constraint in a maximization LP problem, this means:
a. if the coefficient of the objective function is increase by 1 then the RHS for that constraint must be increased by 5
b. if the RHS for that constraint is increased by one then the optimal objective function value is increase by 5
c. if the RHS for that constraint is increased by 5 then the optimal objective function value is increase by 1
d. if the coefficient of the objective function is increase by 5 then the RHS for that constraint must be increased by 1
12. Sensitivity Analysis generally assumes
a. we are considering a change in two input data values at a time
b. are considering a change in only one input data value at a time
c. we are considering several change in several input data…
Suppose an assignment problem, where there are 3 employees who must perform 3 different tasks. The times (in hours) that employees take to perform each of the tasks is shown below. Each employee must perform only one task, and a task can only be performed by one employee. All employees are paid exactly the same wage per hour of work. Minimize the total time to make all tasks.
Task 1 Task 2 Task 3
Employee 1 154 29 40
Employee 2 18 137 12
Employee 3 94 13 31
How many variables does the problem have?
How many constraints does the problem have?
The objective function corresponds to:
Chapter 4 Solutions
Practical Management Science
Ch. 4.2 - Prob. 1PCh. 4.2 - Prob. 2PCh. 4.2 - Prob. 3PCh. 4.2 - Prob. 4PCh. 4.2 - Prob. 5PCh. 4.2 - Prob. 6PCh. 4.3 - Prob. 7PCh. 4.3 - Prob. 8PCh. 4.3 - Prob. 9PCh. 4.3 - Prob. 10P
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