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Tooba Winery produces two types of Shiraz wines: Classy and Plain. Each type of wine consists of High and Low grade grapes. It takes about 2 pounds of grapes to make a bottle of wine. At the start of 2016, the current inventory for each type of wines is as follows (numbers are in Cases of wine. Each case contains 12 bottles of wine) Cases of Wine Classy 120 Plain 180 Tooba Winery is trying to design a production plan for the next 3 years. Each year the winery can produce at most 4000 bottles of wine. At the end of 2018, they want to have at least 200 cases of Classy and 150 cases of Plain (includes wine produced in 2018 and anything leftover from previous years). The projected market size for each product is as follows (numbers are in cases of 12 bottles): 2016 2017 2018 Classy(# of Cases of wine) 90 150 180 Plain (# of Cases of wine) 190 170 240 Wine cannot be sold in the year it is produced. Therefore, in 2016, the winery can only sell the inventory they had at the start of the year. All demand does NOT have to be met. Classy sells for $8/bottle and must consist of at least 70% high-grade grapes. Plain sells for $6/bottle and must consist of at least 60% high-grade grapes. The selling price is fixed over the three year horizon and will not depend on the age of the wine. The proportion of high grade grapes used in producing each type of wine can change from year to year but must meet the constraints of at least 70% high grades in Classy and at least 60% high grade grapes in Plain wine. Tooba Winery can buy grapes from two farmers. Each box of grapes from farmer 1 costs $10 and consists of 4 pounds of high-grade and 2 pounds of low-grade grapes. Each box of grapes from farmer 2 costs $8 and consists of 3 pounds of high-grade and 3 pounds of low-grade grapes. Assume that you can buy fractional boxes from farmers, and that you can make fractional bottles of wine. Further assume that the storage cost for the wine is zero. Formulate a linear programming problem to maximize Tooba’s profit.
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