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 avaailability of only 50 cubic yards of storage space for aging and 125 hours of processing time. Each batch of each type of wine requires 5 cubic yards 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 1 batch but is limited to not more than 7 batches. 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 25% of total wine production must be Merlot. Likewise, at least 25% 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. The company wants to st 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. 1. Determine the optimal solution with the graphical solution method consisting of the following:
A. List all constraints.
B. Graph all constraints.
C. Identify and label feasible region.
D. On top of the graph of the feasible region, overlay contours of the objective function to determine and identify the optimizing direction.
E. Identify and label the corner containing the optimal solution.
F. Explain why the optimal solution is located at this corner.