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2. (4 points) The Sunshine Food Processing Company produces three canned fruit products- mixed fruit x1, fruit cocktail x2, and fruit delight x3. The main ingredients in each product are pears and peaches. Each product is produced in lots and must undergo three processes- mixing, canning, and packaging. The resource requirements for each product and each process are shown in the following linear programming formulation: Maximize 10*1 + 6x2 + 8x3 s. t. 20*, + 10*2 + 16x3 5 320 (pears, lb) 10x1 + 20*2 + 16x3 5 400 (peaches, lb) *1 + 2x2 + 2x3 $ 43 (mixing, hr) *1 + *2 + x3 5 60 (canning, hr) 2x1 + X2 + X3 $ 40 (packaging, hr) X1, X2. X3 20 The optimal simplex tableau is as follows: Basic 10 6 0 0 oooman Variable Quantity x1 x2 x3 $1 x1 8 1 o 0 8/15 1/15 -1/30 16 8/15 -1/30 1/15 3 0 2/15 0 -1/10 36 -1/15 -1/30 -1/30 35 0 -3/5 -1/10 zj 176 10 128/15 7/15 1/15 cj-z ] o -8/15 -7/15 -1/15 a. What is the profit range for mixed fruit that would keep the solution as optimal? b. What is the profit range for fruit delight that would keep the solution as optimal? c. What is the maximum price the company would be willing to pay for additional pears? Over what range is this price valid? d. What is the marginal value of peaches? Over what range is this value valid? e. The company can purchase a new mixing machine that would increase the available mixing time from 43 to 60 hours. Would this affect the optimal solution? f. What is the range for available canning time that would keep the same solution mixture optimal? g. If the manager was to attempt to secure additional units of only one of the resources, which should it be? h. The company is considering producing fruit salad, which would include 15 lbs of pears, 5 Ibs of peaches and requires 30 minutes mixing, 15 minutes canning and 30 minutes of packaging. The profit is expected to be $7 per fruit salad. Would you suggest producing fruit salad? What is the optimal production quantity? i. What are the values of resources (pears, peaches, mixing time, and canning time, packaging time) that are utilized to produce (1) one unit of mixed fruit, (2) one unit of mixed cocktail and (3) mixed delight? j. Write the dual for this problem and state the values of the dual variables at the optimality based on the optimal simplex tableau