EM 605 Spring 2021 Midterm Exam 3/17/2021 The linear programming problem whose output follows is used to determine how many bottles of Hell-bound red nail polish (x1), Blood red nail polish (x2), Bile green nail polish(x3), and Pepto-Bismol pink nail polish(x4) a beauty salon should stock. The objective function measures profit; it's assumed that every piece stocked will be sold. Constraint 1 measures display space in units. Constraint 2 measures time to set up the display in minutes. (Bile green nail polish does not require any time to prepare its display). Constraints 3 and 4 are marketing restrictions. Constraint 3 indicates that the maximum demand for Hell-bound red and Bile green polish is 25 bottles. Constraint 4 specifies that the minimum demand for Blood red, Bile green and Pepto-Bismol pink nail polish bottles combined is at least 50 bottles. MAX 100x1 + 120x2 + 150x3 + 125x4 such that : x1 + 2x2 + 2x3 + 2x4 $ 110 Optimal Solution: 3x1 + 5x2 + x4 $ 120 Objective Function Value = $7,625.00 x1 + x3 $ 25 X2 + x3 + X4 > 50 x1, X2 , X3, X4 2 0 Objective Cell (Max) Variable Cells Cell Name Original Value Final Value Final Reduced Objective Allowable Allowable $IS9 Profit 7625 Call Name Value Cost Coefficient Increase Decrease Variable Cells SD$9 X1 10 0 100 10+30 12.5 Name Original Value Final Value Integer SE$9 X2 0 -5 120 16+30 SDS9 X1 10 Contin 0 150 0 12. 2's SES9 X2 0 0 Contin 5G59 X4 35 125 25 SF$9 X3 0 15 Contin SG$9 X4 35 Contin Constraints Final Shadow Constraint Allowable Allowable Constraints Cell Name Value Price R.H. Side Increase Decrease Cell Name Cell Value Formula Status Slack 110 110 $1511 Space 75 110 51511