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Beer Etc, Mallory Furniture: Linear Programming Model and Sensitivity Analysis

1. The production manager for Beer Etc. produces 2 kinds of beer: light (L) and dark(D). Two resources used to produce beer are malt and wheat. He can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week respectively. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. What is the objective function?
Z = $1L + $2D
Z = $4L + $8D
Z = $12L + $8D
Z = $2L + $1D
Z = 12 lbs + 4 lbs

2. The production manager for Beer Etc. produces 2 kinds of beer: light (L) and dark(D). Two resources used to produce beer are malt and wheat. He can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week respectively. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. What is the malt constraint?

3. The production manager for Beer Etc. produces 2 kinds of beer: light (L) and dark(D). Two resources used to produce beer are malt and wheat. He can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week respectively. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. What is the wheat constraint?

4. Sensitivity analysis is the analysis of the effect of __________ changes on the __________.
price, company
cost, production
parameter, optimal solution
none of the above

5. Mallory Furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the storage space constraint?

Solution Preview

1. The production manager for Beer etc. produces 2 kinds of beer: light (L) and dark(D). Two resources used to produce beer are malt and wheat. He can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week respectively. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. What is the objective function? (Points :2)
Z = $1L + $2D
Z = $4L + $8D
Z = $12L + $8D
Z = $2L + $1D
Z = 12 lbs + 4 lbs

Answer:

Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle

Objective function will be

Z = $2L + $1D

2. The production ...

Solution Summary

The objective function is determined for a Beer company. The objective function allows for the malt constraint to be found.

$2.19