The Mason Wine Company produces two kinds of wine Mason Blanc and Mason Merlot. The...

   

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The Mason Wine Company produces two kinds of wine – Mason Blanc and Mason Merlot. The wines are produced in 1,000-gallon batches. The profit for a batch of Blanc is $12,000 and the profit for a batch of Merlot is $9,000. The wines are produced from 64 tons of grapes that the company has acquired. A 1,000-gallon batch of Blanc requires 4 tons of grapes and a batch of Merlot requires 8 tons. However, the production is limited by the availability of only 50 cubic yards (yd') of storage space for aging and 120 hours of processing time. Each batch of each type of wine requires 5 yd' of storage space. The processing time for a batch of Blanc is 15 hours and the processing time for a batch of Merlot is 8 hours. The wine company will not produce more or less than the range of amounts demanded for each type. Demand for each type of wine is for at least I batch but is limited to not more than 7 batches. Even so, the demand for Blanc is the same as or is higher than the demand for Merlot. Company executives do not want to depend on just one type of wine so they have mandated minimum production levels of both types of wine. Specifically, at least 20% of the total wine production must be Merlot. Likewise, at least 20% of the total wine production must be Blanc. Moreover, the amount of the Merlot produced should not be more than half of the total production. Also, the break-even point on profit is $54,000. Therefore, company requires that it must make at least $54,000 in profit to do better than just break even (that is, profit must be $54,000 or more). The company wants to set the production levels, in terms of the number of 1,000- gallon batches of both the Blanc and Merlot wines to produce so as to earn the most profit possible. (NOTE: Partial [i.e., fractional] batches can be produced; they refer to pending production. If fractional, round the optimal solution values to two (2) decimal places.) Formulate this problem mathematically. Make certain to: a. define the decision variables. b. state the objective function in terms of your decision variables. c. state all of the constraints in terms of your decision variables. In lines entered below this part, state your mathematical representation. In lines entered below this part, state the specific type of problem this is. Include an explanation of why. The Mason Wine Company produces two kinds of wine – Mason Blanc and Mason Merlot. The wines are produced in 1,000-gallon batches. The profit for a batch of Blanc is $12,000 and the profit for a batch of Merlot is $9,000. The wines are produced from 64 tons of grapes that the company has acquired. A 1,000-gallon batch of Blanc requires 4 tons of grapes and a batch of Merlot requires 8 tons. However, the production is limited by the availability of only 50 cubic yards (yd') of storage space for aging and 120 hours of processing time. Each batch of each type of wine requires 5 yd' of storage space. The processing time for a batch of Blanc is 15 hours and the processing time for a batch of Merlot is 8 hours. The wine company will not produce more or less than the range of amounts demanded for each type. Demand for each type of wine is for at least I batch but is limited to not more than 7 batches. Even so, the demand for Blanc is the same as or is higher than the demand for Merlot. Company executives do not want to depend on just one type of wine so they have mandated minimum production levels of both types of wine. Specifically, at least 20% of the total wine production must be Merlot. Likewise, at least 20% of the total wine production must be Blanc. Moreover, the amount of the Merlot produced should not be more than half of the total production. Also, the break-even point on profit is $54,000. Therefore, company requires that it must make at least $54,000 in profit to do better than just break even (that is, profit must be $54,000 or more). The company wants to set the production levels, in terms of the number of 1,000- gallon batches of both the Blanc and Merlot wines to produce so as to earn the most profit possible. (NOTE: Partial [i.e., fractional] batches can be produced; they refer to pending production. If fractional, round the optimal solution values to two (2) decimal places.) Formulate this problem mathematically. Make certain to: a. define the decision variables. b. state the objective function in terms of your decision variables. c. state all of the constraints in terms of your decision variables. In lines entered below this part, state your mathematical representation. In lines entered below this part, state the specific type of problem this is. Include an explanation of why.

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