A. Suppose we decided to run the machine for an additional hour each week. How much would the profit change? Be sure to show your work and fully jus- tify your response!

B.Suppose we run the machine for an additional 3 hours each week. Provide an upper and lower bound on how much the optimal profit might change. Justify your response quantitatively.

C. Suppose you removed the Flagship constraint that required twice as much Bold blend as as Strong blend. Would the optimal profit go down, go up or stay the same? Justify your response quantitatively. If it is not possible to say from the info given, explain why.

A friend uses Excel to solve the resulting linear optimization problem. The sensitivity analysis tables are below. You'll notice one of the Shadow Prices is missing and re- placed with an "XXX." Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Coefficient Increase Decrease $C$20 Number Produced Mild 25.00 0.00 20.00 1E+30 5.88 $D$20 Number Produced Bold 25.00 0.00 14.00 1E+30 0.32 $E$20 Number Produced Strong 12.50 0.00 15.00 1E+30 0.65 $F$20 Number Produced Intense 15.44 0.00 16.00 0.24 16.00 Cost Constraints Shadow Price Cell Name $C$18 Storage $C$22 Flagship $C$25 Marketing Mild $C$26 Marketing Bold $C$27 Marketing Strong $C$28 Marketing Intense $C$9 Machine Time Final Value 34.04 0.00 25.00 25.00 12.50 15.44 1200.00 XXXX -1.38 5.88 0.32 0.00 0.00 0.94 Constraint R.H. Side 50.00 0.00 25.00 25.00 25.00 25.00 1200.00 Allowable Increase 1E+30 25.00 17.50 11.67 1E+30 1E+30 162.50 Allowable Decrease 15.96 25.00 10.83 7.22 12.50 9.56 262.50