Problem 8: Given the following linear programming results for a profit maximization problem. In this problem, the choice variables (xi) are inputs; the firm must choose the optimal amount of each input to keep total costs at a minimum. The constraints (bi) represent production (output) of three products shirts, pants, and shoes. B D E F G 3 X1 0.00 2 H TC 101.25 X2 5.94 12 4 Input 5 Per Unit Input Cost 6 0.00 7.50 4 5 7 X2 X3 X4 Resource Usage Resource Usage 8 2 3 8 Constraints 9 Output 1 (Shirts) 10 Output 2 (Pants) 11 Output 3 (Shoes) Total LHS 70.00 2 73.13 > 100.00 RHS 70 40 100 Slack 0.00 33.13 0.00 8 6 4 u 2 8 4 7 Variable Cells Name Cell $B$4 Input x1 $C$4 Input x2 $D$4 Input x3 $E$4 Input x4 Final Value 0 5.9375 0 7.5 Reduced Objective Cost Coefficient 0.625 2 0 12 2.25 5 0 4 Allowable Allowable Increase Decrease 1E+30 0.625 20 1.333333333 1E+30 2.25 0.5 1E+30 Constraints Cell Name $F$11 Output 3 (Shoes) Total LHS $F$9 Output 1 (Shirts) Total LHS $F$10 Output 2 (Pants) Total LHS Final Value 100 70 73.125 Shadow Constraint Allowable Allowable Price R.H. Side Increase Decrease -0.125 100 63.33333333 30 1.625 70 30 27.14285714 0 40 33.125 1E+30 (a) (b) (C) (d) Write the linear program implied by the results above. What will happen to TC if the firm hires one unit of input xz? Explain this result. What will happen to TC if the firm produces one more unit of output 1 (shirts), b? What will happen to TC if the firm produces one more unit of output 2, bz