Volcano Potato Company (VPC) grows potatoes, processes them, and then sells three potato products: fresh potatoes, frozen french fried potatoes, and frozen hash ball potatoes (shredded and then reconstituted balls of potatoes with a soft consistency). During the next two months, VPC expects to harvest 8 million pounds of potatoes. VPC would like to determine how much of each product should be made from the potatoes. Potatoes are graded according to quality on a 0-5 scale. VPC divides its potatoes into three grades: A, B, and C. Grade A potatoes have an average quality rating of 4.5; grade B potatoes have an average quality rating of 2.5, and grade C potatoes have a quality rating below 1 and are not used for any products. From historical data and estimates based on the current growing season's weather,VPC believes the distribution of potato quality will be:
A=50
B=40
C=10
Percentage of harvest

Fresh potatoes earn a profit of $0.40 per pound after processing costs, but only grade A potatoes can be sold as fresh potatoes. Frozen french fried potatoes earn $0.32 per pound after processing costs, but the potatoes used must have an average quality rating of at least 3.5. Hash balls earn $0.25 per pound after processing costs, but the potatoes used must have an average quality rating of at least 3.0. Assume that these ratings are linear in the sense that the quality rating of a mixture equals the weighted average of the inputs.VPC believes it can sell as much french fried and hash ball potatoes as it can make, but it believes the total demand for its fresh potatoes during the next two months is 2.5 million pounds
(a) Formulate a linear programming model to determine the best use for the potatoes so as to maximize VPC's profit.
(b) Solve the problem using a computer and explain the answer in words
(c)Suppose VPC could buy additional grade A potatoes at $0.35 per pound; how much should it buy? Explain.

Answer rating: 100% (QA)

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