Is B=15, R=30, S=10: Blueberries Raspberries Strawberries Profit contribution pe

Question

Is B=15, R=30, S=10: Blueberries Raspberries Strawberries Profit contribution per Acre $6,700.00 $7450.00 $7,100.00 Resource Available Resources Used per Unit Produced Used land Water Fertilizer Max storage for Strawberries Min for Strawberries 55 S 385 10 0 0 S500 30 2 L 7.5 14 790 820 10 S 0 Blueberries RaspberriesStrawberries 30 Acres 15 10 Is B=15, R=30, s-10: The optimal solution? A feasible but not optimal solution? An infeasible solution? Multiple optima solution? Briefly explain your answer

Explanation / Answer

The answer is “a feasible but not optimal solution”.

In the provided solution Blueberries = 15, Raspberries = 30 and Strawberries = 10.

Thus total profit = 6700*15 + 7450*30 + 7100*10

= $395,000.

Here all constraints are satisfied as well.

But if the problem is solved we will get the maximum profit as a different number. The problem is:

Let the variables be b,r,s (for blueberries, raspberries and strawberries respectively).

Objective function: To maximize 6700b+7450r+7100s

Constraints are:

1. b+r+s<=66

2. 5b+8r+7s<=500

3. 10b+14r+22s<=820

4. s<=30

5. s>=7.5

Solving in solver using excel we get the following solution:

B R S 41.00 17.50 7.50 Formula Total profit 458,325.00 6700b+7450r+7100s Constraints 66.00 <= 66.00 b+r+s<=66 397.50 <= 500.00 5b+8r+7s<=500 820.00 <= 820.00 10b+14r+22s<=820 7.50 <= 30.00 s<=30 7.50 >= 7.50 s>=7.5

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