Linear Programming Case Study

In: Business and Management

Submitted By ijenkin
Words 331
Pages 2
The owner of Chips etc. produces 2 kinds of chips: Lime (L) and Vinegar (V). He has a limited amount of the 3 ingredients used to produce these chips available for his next production run: 4600 ounces of salt, 9400 ounces of flour, and 2200 ounces of herbs. A bag of Lime chips requires 1.5 ounces of salt, 5 ounces of flour, and 2 ounces of herbs to produce; while a bag of Vinegar chips requires 4 ounces of salt, 6 ounces of flour, and 2 ounces of herbs. Profits for a bag of Lime chips are $0.48, and for a bag of Vinegar chips $0.59.
a) What is the formulation for this problem?
b) For the production combination of 800 bags of Lime and 600 bags of Vinegar, which resource is not completely used up and how much is remaining?
c) For the production combination of 800 bags of Lime and 600 bags of Vinegar, which resource is not completely used up and how much is remaining?
d) Discuss: Slack (if any); shadow price, and sensitivity analysis results using the program of your choice. Above problem is a maximization problem as one is trying to maximize the profits by making different bags of chips. It takes salt, flour and herbs to make two different types of chips – Lime and Vinegar. There are constrained amounts of salt, flour and herb and the owner want to maximize his profits. The amount of profit per bag is given as well.

The LP problem thus becomes:
Maximize Profits from the sale of bags of both lime and vinegar chips
Constraints:
1. Salt consumed should not exceed 4,600
2. Flour consumed should not exceed 9,400
3. Herbs consumed should not exceed 2,200
In mathematical terms, let’s say X1 to be the number of Lime bags and X2 to be the number of Vinegar bags.
LP is:
Maximize: 0.48 X1 + 0.59 X2
Subject to:
1.5X1 + 4…...

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