Assignment # 3 Solutions
LP Case Study

Data Analysis:

Solution:

Incorrect Statements

Using the rating system, only 800,000 pounds of whole tomatoes can be used.
This is because the equation for canned whole tomatoes is
[pic]
It follows that, as A tomatoes can be 600,000 maximum, that solving for B (i.e. solving for x2 when x1 = 600,000) would equate it to 200,000 pounds. Therefore, total can only be 800,000 pounds of whole canned tomatoes used.

In this case, Myers has used a different allocation of costs that have already been paid. These should not influence the decision on product mix.

Model formation

Define: (these definitions were given to students)
Pounds of quality A in whole tomatoes[pic],
Pounds of quality B in whole tomatoes[pic],
Pounds of quality A in juice[pic],
Pounds of quality B in juice[pic],
Pounds of quality A in paste [pic],
Pounds of quality B in paste [pic]
Preliminary Calculations: Objective Coefficients: Canned: $1.48/case, 18 pounds/case [pic] Juice: $1.32/case, 20 pounds/case [pic] Paste: $1.85/case, 25 pounds/case = [pic]

Quality Requirements:

Whole: [pic], so therefore [pic] Juice: [pic], so therefore [pic]

Demand: to calculate, multiple forecast by pounds per case = 14,400,000

Maximize: [pic]

Constraints:
[pic]

Solution (student need to provide a managerial statement and do interpretation of the solution)

[pic]

|Produce |700000 | Pounds of whole tomatoes |
|Produce |300000 | Pounds of Juice |
|Produce |2000000 | Pounds of paste |

|Total Profit: |$225,340.00 |
|Cost of tomatoes: |$180,000.00 |
|Net Profit: |$45,340.00 |

[pic]

This the Excel solver sensitivity reports
[pic]
Zero (i.e. Red Brand Canner is willing to pay nothing for such a campaign).
Justification: Since Shadow price = 0 or since there is already slack in the demand for juice constraint

Shadow price on Grade B supply constraint is $0.0579 for up to an additional 466,666.67 pounds. Thus would be willing to pay 50,000*0.0579 = $2,895 for the entire 50,000 pounds.

The suggested change will increase the price of juice by $0.10/20 = 0.005. Although this is within the allowable increases on the