Problem 2 A manufacturer has three plants with access production capacity. It can use this capacity to produce a product that comes in three sizes, Large, Medium, and Small. The profit from selling the product depends on its size. The forecast of sales for each product size is known to be 900, 1200, 750 units for the Large, Medium and Small products respectively, so production levels should not exceed these values. There is a limited daily storage available in each plant, which limits the production levels in each plant. To prevent layoffs management wants the percent of the available capacity used for production be equal among all plants (for example, capacity in plant 1 is 750 units. If this plant produces 500 units, it uses 500/750 = .66 of its capacity. Then all plants should have the same percentage of their own capacities used) Observe some more required information. Capacity avail Storage avail Plant1 750 units 900 13000 sqft 12000 Profit/unit Storage/unit Plant2 Large $420 Medium Small 360 300 20 sq-ft 15 12 2.1 Write the linear programming model in the Answers sheet. Plant3 450 5000 The sensitivity report for this model is provided in the Answers sheet. Answer the following sensitivity questions. 2.2 How much the unit profit of the large size product produced in plant 1 can change, before the current production changes? a. Any change in the unit profit will change the optimal production plan b. From the sensitivity report the change is 888.88. c. Two coefficients are changing. (i) Plant 1= 750.; (ii) Large product = 750 0/750 + 55.55/750 < 1. No change in the coefficients. 2.3 How much should the company be willing to pay for 100 sq-ft of additional storage in each plant, when each addition is considered individually? a. The company should not pay any amount in plant 1, any amount in plant 2, and 291 dollars in plant 3. b. The company should pay any amount charged in plant 1, any amount charged in plant 2, and 291.67 dollars in plant 3. c. The company should not pay any amount in either plant 1 or plant 2, and 291.67 dollars in plant 3. d. The company should pay 888.88/100 dollars in plant 1, 1416.67/100 dollars in plant 2, and 2333.33/100 dollars in plant 3. 2.4 If all the sales estimates are too optimistic by 10%, the total profit must be inflated. Can oyu re-calculate the total profit without a re-run of the model? a. There is no need to re-run the model because no selling price is changing. b. We must re-run the model. The total demand for all the three products is inflated by 3*10% = 30%, and this is greater than any allowable increase. c. Three constraints are changing. We need to apply the SumRate rule. After applying it properly, the answer is "Yes". We do not have to re-run the model. Explanain in the answers sheet. d. Three constraints are changing. We need to apply the SumRate rule. After applying it properly, the answer is "Yes". We do not have to re-run the model. Explanain in the answers sheet.