Assignment. Linear Programming Case Study
A beauty salon tries to determine how many bottles of fire red nail polish, bright red nail polish, basil green nail polish, and basic pink nail polish to stock. The profits for each nail polish; assumming that every piece stocked will be sold, are as follows: $100 per bottle of fire red nail polish, $120 per bottle of bright red nail polish, $150 per bottle of basil green nail polish, and $125 per bottle of basic pink nail polish. The display space and set up time requirements are listed in the table. Note that green nail polish does not require any time to prepare its display.
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Display requirements
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fire red
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bright red
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basil green
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basic pink
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available
|
|
Display space (units)
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1
|
2
|
2
|
2
|
108
|
|
Time to set up a display (minutes)
|
3
|
5
|
|
1
|
120
|
The maximum demand combined for fire red and green polish is 25 bottles, while the minimum demand combined for bright red, green and pink nail polish bottles is at least 50 bottles.
a) Formulate the Linear Programming model for this problem
b) Solve the problem using Excel Solver or QM for Windows
c) How many bottles of fire red nail polish, bright red nail polish, basil green polish and pink nail polish should be stocked?
d) What is the maximum profit?
e) How much space will be left unused?
f) How many minutes of idle time remaining for setting up the display?
g) To what value can the per bottle profit on fire red nail polish drop before the solution would change?
h) By how much can the per bottle profit on green basil nail polish increase before the solution would change?
i) Is it possible for saloon to increase the profit by getting more display space or using more time for setting up the displays?
Please turning in two deliverables, a short writeup of the project and the spreadsheet or QM for Windows file showing your work.
Write up.
Your write up should introduce your solution to the project by describing the problem. Correctly identify what type of problem this is. For example, you should note if the problem is a maximization or minimization problem, as well as identify the resources that constrain the solution. Identify each variable and explain the criteria involved in setting up the model. This should be encapsulated in one (1) or two (2) succinct paragraphs.
After the introductory paragraph, write out the L.P. model for the problem. Include the objective function and all constraints, including any non-negativity constraints. Then, you should present the optimal solution, based on your work in Excel/QM for Windows. Explain what the results mean.
Finally, write a paragraph addressing the part of the problem pertaining to sensitivity analysis and shadow price.