Problems:
Introduction to Management Problems
Problem 1
A graphical representation of a linear program is shown in the attachment. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function.
a) If this is maximization, which extreme point is the optimal solution? Explain your answer.
b) If this is a minimization, which extreme point is the optimal solution? Explain your answer.
c) What would be the new slope of the objective function if multiple optimal solutions occurred along line segment AB? Explain your answer.
d) Assuming this is a maximization problem, by how much can the coefficient of X in the objective function be increased before the optimal solution changes? Explain your answer.
e) Assuming this is a maximization problem, by how much can the coefficient of X in the objective function be reduced before the optimal solution changes? Explain your answer.
Problem 2
Bullseye Shirt Company makes three types of shirts: Athletic, Varsity, and Surfer. The shirts are made from different combinations of cotton and rayon. The cost per yard of cotton is $5 and the cost for rayon is $7. Bullseye can receive up to 4,000 yards of cotton and 3,000 yards of rayon per week.
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Shirt
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Total Yards of fabric per shirt
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Fabric requirement
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Minimum weekly contracts
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Maximum Demand
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Selling Price
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|
Athletic
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1.00
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at least 60% cotton
|
500
|
600
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$30
|
|
Varsity
|
1.20
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no more than 30% rayon
|
650
|
850
|
$40
|
|
Surfer
|
0.90
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As much as 80% cotton
|
300
|
700
|
$36
|
a) Formulate a linear program to maximize the company's profit and put it in standard format. Clearly define your decisions variables, objective function and constraints.
b) Implement your formulation in Excel and use Solver to find the optimal solution. Provide answers for the optimal amounts of different shirt types.
c) Based on the sensitivity analysis report, by how much can you reduce the price of the Athletic shirts before the optimal solution changes? Justify your answer.
d) In the optimal solution, how much more cotton and rayon would be left, if any?
e) If there is a 50% shortage in cotton and rayon, what impact does this have on your solution? Provide an explanation based on your current solution and not by resolving the problem.
f) If you can secure some free marketing only for one shirt type of your choice to increase its maximum weekly demand, which one would you choose and why?