QUESTION $5$

Crown Corn Company $($CCC$)$ grows corn, processes it$,$ and then sells four corn products: fresh corn on the cob, frozen corn nibblets, corn starch and cornmeal. During the next three

months, CCC expects to harvest $15$ million pounds of corn. CCC would like to determine how much of each product should be made from the corn. Corn is graded according to quality on

a $0-10$ scale. CCC divides its corn into three grades: A$,$ B$,$ C and D$.$ Grade A corn has an average quality rating of $9$; grade B corn has an average quality rating of $7\mathrm{.}5,$ grade C corn has an

average quality rating of $6,$ and grade D corn has a quality rating below $4$ and is not used for any products. From historical data and estimates based on the current growing season's

weather, CCC believes the distribution of corn quality will be: $40\%$ grade A$,25\%$ grade B$,25\%$ grade C and $10\%$ grade D$.$

Fresh corn on the cob earn a profit of $$0\mathrm{.}85$ per pound after processing costs, but only grade A corn can be sold as fresh corn on the cob. Frozen corn nibblets earn $$0\mathrm{.}72$ per pound

after processing costs, but the corn used must have an average quality rating of at least $8.$ Corn starch earns $$0\mathrm{.}57$ per pound after processing costs, but the corn used must have an

average quality rating of at least $7.$ Cornmeal earns $$0\mathrm{.}53$ per pound after processing costs, but the corn used must have an average quality rating of at least $5\mathrm{.}5.$ Assume that these

ratings are linear in the sense that the quality rating of a mixture equals the weighted average of the inputs. CCC believes it can sell as much corn nibblets, corn starch and cornmeal as it

can make, but it believes the total demand for its fresh Corn on the cob during the next three months is $3$ million pounds.

Formulate a linear programming model to determine the best use for the corn so as to maximize CCC$\text{'}$s profit and use EXCEL SOLVER $($use images of excel solver to show the process$)$