An up-and-coming drug company needs to decide production levels for the upcoming week. Suppose now the company sells 5 types of drugs, Jomentum, Zapitol, Pakoderm, Kioal, and Diadol. Each drug is produced in batches. The labor requirements, selling price, and production costs are given below. The company has 4000 hours of manufacturing labor available and 3200 hours of quality testing labor available. Batch Selling Price Batch Production Cost Labor hours required/ batch Quality Testing Drug 1. Jomentum 2. Zapitol 3. Pakoderm Manufacturing $98 $48 40 16 $106 $76 18 $79 $39 32 18 4. Kiodal 5. Diadol Weekly capacity (labor hours) $56 $46 16 6 $42 $32 28 12 4000 3200 Assume that all product made is sold. For the purposes of this problem, assume that fractional values of the decision variables are acceptable. Let x, be the number of batches of drug i made each week, i=1..., 5. An LP fomulation that will provide the number of batches of drugs of each type to be sold follows: Max profit = 50x, + 30x, + 40x, +10x, +10x, St. 40x, +5x, 16x, +18x, +18x, +6x, +12x, < 3200 (Quality Constraint) x, 20 vi +32x; +16x, +28.x, < 4000 (Manufacturing constraint) Using sensitivity analysis concepts learned in class, we will answer the following question, without excel. a. Verify that the profit optimizing solution requires drugs Jomentum and Zapitol to be made while Pakoderm, Kioal, and Diadol are not. b. What is the optimal profit and quantities to be made? c. How much money am I willing to pay to increase the number of quality test labor hours available to 4000?