OPRE 3333 - Homework 5 3 Question 2. (20 points) A beverage cans manufacturer makes 3 types of soft drink cans needed for the beverage producers to fill soft drinks of three different volumes. The maximum availability of the machines' time allotted per day is 90 hours and the supply of metal is limited to 120 kg per day. The following table provides the details of the input needed to manufacture one batch of cans. Cans Large Medium Small Maximum Metal (kg)/batch 9 6 5 5 120 Machines' Time (hr)/batch 4.4 4.2 4 90 Profit/batch $50 $45 $42 The manufacturer is interested in maximizing the total profit per day. The sensitivity report provided below was generated using the Excel Solver to determine the optimal solution to this problem. Using the sensitivity report, answer the following questions: 9 6 Variable Cells 7 Final Reduced objective Allowable Allowable 8 Cell Name Value Cost Coefficient Increase Decrease 9 SASI 0 -0.4 50 0.4 1E+30 10 $B$1 10 0 45 5.4 0.085714286 11 $C$1 12 0 42 0.105263158 4.5 12 14 13 Constraints 14 Final Shadow Constraint Allowable Allowable 15 Cell Name Value Price R.H. Side Increase Decrease 16 $D$3 120 1.2 120 8.571428571 7.5 17 $D$4 90 9 90 6 6 (a) Optimal production quantity of small can per day: (b) Optimal profit per day: (c) Will the current optimal solution stay optimal if the unit profit of large can decreases to 40? (Yes or No) (d) Will the current optimal solution stay optimal if the unit profit of small can increases to 45? (Yes or No) (e) Will the current optimal solution stay optimal if we add a constraint that says pro- duction quantity of medium can per day should be at least 15? (Yes or No) (f) Will the shadow price of the constraint related to the supply of metal remain valid if we decrease the available supply to 110 kg per day? (Yes or No) (g) Calculate the effect on the total profit of increasing the supply of metal to 125 kg per day. (h) Calculate the effect on the total profit of decreasing the machine available time to 85 hours per day