What is the maximum profit under the optimal solution? 

 

An up-and-coming drug company needs to decide production levels for the upcoming week. The company sells three types of drugs, Jomentum, Zapitol, and Pakoderm, each of which is produced in batches. The labor requirements, profit per batch, and weekly demand for each type of drug is given below, along with the company's weekly capacity (labor hours). Labor hours required/batch Drug Profit per batch Manufacturing Quality Testing Weekly Demand Jomentum 29 30 13 52 Zapitol Pakoderm 21 25 8 130 62 32 19 67 4000 3200 Weekly capacity (labor hours) The output for an LP solution is provided below. Adjustable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$12 Production Jomentum 52 0 29 1E+30 3.80 $C$12 Production Zapitol 12 0 21 3.17 21 $D$12 Production Pakoderm 67 0 62 1E+30 83.12 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $G$24 Jomentum Demand $G$25 Zapitol Demand $G$26 Pakoderm Demand 226 52 4 52 9.87 52 12 0 130 1E+30 118.16 67 83 67 9.25 67 $B$25 Manufacturing Needed 4000 1 4000 2954 296 $B$26 Quality Testing Needed 2044 0 3200 1E+30 1156.28 The objective is to come up with the production volumes (number of batches) of the three products to maximize profit. We denote the production volumes of Jometum, Zapitol, and Pakoderm by X,, X, and Xp, respectively.