Question

The Valley Wine Company produces two kinds of wine—Valley Nectar and Valley Red. The wines are produced from 64 tons of grapes the company has acquired this season. A 1,000-gallon batch of Nectar requires 4 tons of grapes, and a batch of Red requires 8 tons. However, production is lim- ited by the availability of only 50 cubic yards of storage space for aging and 120 hours of process- ing time. A batch of each type of wine requires 5 cubic yards of storage space. The processing time for a batch of Nectar is 15 hours, and the processing time for a batch of Red is 8 hours. Demand for each type of wine is limited to seven batches. The profit for a batch of Nectar is $9,000, and the profit for a batch of Red is $12,000. The company wants to determine the number of 1,000-gallon batches of Nectar ( x 1 ) and Red ( x 2 ) to produce in order to maximize profit.Formulate a linear programming model for this problem.Solve this model by using graphical analysis.

Answer 1

Answer:

maximize 9000n + 12000r

constraints:

• 4n + 8r ≤ 64
• 5n + 5r ≤ 50
• 15n + 8r ≤ 120
• n ≤ 7
• r ≤ 7
• n ≥ 0
• r ≥ 0  

     

using solver, the solution is:

4 1,000 gallon batches of nectar wine and 6 1,000 gallon batches of red wine

maximum profit = (4 x $9,000) + (6 x $12,000) = $108,000