Ms Workshop

1. We used solver to give the optimal solution (Exhibit 1).We set the allocation number as variable cells and we set three constraints which are 1, Total required number must <= number available 2, Total production <= Demand 3, Total quality >= Total quality required. Then solver gave us the solution which is: 700,000 pounds of “Whole Tomatoes” with 525,000 pounds of grade A tomatoes and 175,000 pounds of grade B. 300,000 pounds of “Tomato Juice” with 75,000 pounds of grade A and 225,000 pounds of grade B. 2,000,000 pounds of “Tomato Paste” with all grade B.
2. According to the result of “Solver”, we seek for maximum contribution under all the constraints. It turned out that $676,067 is the largest contribution we can acquire. Once any of the number changed, the contribution will be lower than what we acquired from this result. So we are sure that our recommendation is the best possible one.

1. Yes, he should buy the additional A tomatoes because the total contribution is $676,067 before the additional A tomatoes are purchased. Once the additional A tomatoes are purchased, the total contribution will increase to $697,080. (Exhibit 2)
2. To acquire the best result of total contribution, the 80,000 pounds of additional A tomatoes should be all allocated to “Whole Tomatoes”.

2-3.   The result which is generated by Solver is the only one optimal allocation. The reason is that once any numbers within adjustable cells changes, the total contribution will decrease. The whole model is based on linear relation so there is only one optimal allocation under these constraints.

2-4.   According to the repeated trial (Exhibit 3), once the cost of the additional A tomatoes increases to 51.8 cents/ pound, the total contribution will be the same as no additional A tomatoes are involved. That means if the price is more than 51.8 cents/pound, they will earn less money than no additional A tomatoes. So up to 51.8 cents/ pound should Gorden be willing to pay.

3-1.   As we can see from the former model, only paste production reaches the limitation of the demand, which means there is potential profit in paste production. When 5,000 cases increases on “Tomato Paste”, the total contribution will increase by $6,042.(Exhibit 4) It means that RBC is willing to pay less than 6,042 for the campaign.

3-2.   Compared to the original total contribution, only when the demand of paste increases, the total contribution will increase. Otherwise, the contribution doesn’t change. And we could confirm it by applying Solver. According to the analysis result of “Solver”, the optimal decision is to allocate all the 5,000 cases to “Tomato Paste”. The advertising is suggested directed at the “Tomato Paste”.