Problem #1 Solve the following linear programming model graphically: Maximize Z = 3x2 + 6x2 Subject to 3x + 2x2 s 18 X1 + X2 2 5 xy S4 X1, X220 Problem #2 The Valley Wine Company produces two kind 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 limited by the availability of only 50 cubic yards of storage space for aging and 120 hours of processing 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 (X1) and Red (X2 ) to produce in order to maximize the profit. Solve this linear programming model graphically