RED BRAND CANNERS CASES

We first saw the Red Brand Canners (RBC) case in Chapter 3 , where the model was formulated and assumptions were discussed. In the following questions, the analysis continues. You are asked to solve several formulations in Excel and then analyze the Solver Sensitivity Reports.

Questions

1. Use Solver to optimize your LP formulation of the Red Brand Canners production model. Do not include the option of purchasing up to 80,000 additional pounds of grade A tomatoes.
2. What is the net profit obtained after netting out the cost of the crop?
3. Myers has proposed that the net profit obtained from his policy would be $\$ 144,000$. Is this true? If not, what is his net profit (taking into account, as in Question 2 the cost of the crop)?
4. Suppose Cooper suggests that, in keeping with his accounting scheme as advanced in Exhibit 2 of the original case, the crop cost of 18 cents per pound should be subtracted from each coefficient in the objective function. Change your formulation accordingly, and again solve the model. You should obtain an optimal objective value that is greater than that obtained in Question 2 .
   Explain this apparent discrepancy (assume that unused tomatoes will spoil).
5. Suppose that unused tomatoes could be resold at 18 cents per pound. Which solution would be preferred under these conditions? How much can the resale price be lowered without affecting this preference?
6. Use the Sensitivity Report from Question 1 to determine whether the additional purchase of up to 80,000 pounds of grade A tomatoes should be undertaken. Can you tell how much should be purchased?
7. Use a reformulated model to obtain an optimal product mix using the additional purchase option. The solution to your reformulated model should explicitly show how the additional purchase should be used.
8. Suppose that in Question 1 the Market Research Department feels it could increase the demand for juice by 25,000 cases by means of an advertising campaign. How much should Red Brand be willing to pay for such a campaign?
9. Suppose in Question 1 that the price of juice increased 30 cents per case. Does your Solver Sensitivity Report tell you whether the optimal production plan will change?
10. Suppose that RBC is forced to reduce the size of the product line in tomato-based products to 2 . Would you need to rerun the Solver to tell which product should be dropped from the line?
11. Suppose that in Question 1 an additional lot of grade B tomatoes is available. The lot is 50,000 pounds. How much should RBC be willing to pay for this lot of grade \(B\) tomatoes?

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