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Red Brand Case

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6. Is it advisable to purchase any of the available 100,000 lbs of grade A tomatoes? (use the sensitivity report from question 2). If so, (a) how much should we buy? (b) How will the additional tomatoes be used?

In order to figure out if we should buy and by how much we should purchase, we made some modifications associated with our model. First of all, we need to add one more decision variable, Additional A, which is the amount of extra grade A tomatoes we decide to purchase. Then we need to change the profit formula to subtract additional purchase cost, which is $0.15*Additional A, the deal Gordon had to purchase up to 100,000 lbs. grade A tomatoes. Also, we need to change the constraint for A grade tomatoes from 600,000 lbs. to (600,000+Additional A) lbs. The last step is to add another constraint to make the decision variable Additional A can be no more than 100,000 lbs.
When we ran sensitivity analysis, the shadow price for grade A tomatoes is $0.27, which means when the company increases 1 lb. of grade A tomatoes available in production process, the total profit will increase by $0.27. So as long as the purchase price less than the shadow price, company should purchase extra grade A tomatoes. Moreover, the allowable increase for constraint of amount of grade A tomatoes available is 1,400,000. It means any amount of additional grade A tomatoes under 1,400,000 lbs. will be feasible to purchase to increase profit. Thus it is a good idea to purchase whole 100,000 lbs. grade A tomatoes with the cost of 15 cents and use them all into production of canned whole tomatoes.

7. Through additional advertising, we can increase demand for juice by 25,000 cases. What is the maximum we would be willing to spend on an advertising campaign for juice?

Since the amount of grade A tomatoes is the constraint and the net profit of whole tomatoes per case is greater…...

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