Question 3: (40 pts) Starbright Coffee Shop serves two coffee blends it brews on a daily basis, Pomona and Coastal. Each is a blend of three high-quality coffees from Colombia, Kenya, and Indonesia. The coffee shop has 6 pounds of each of these coffees available each day. Each pound of coffee will produce sixteen 16 ounce cups of coffee. The shop has enough brewing capacity to brew 30 gallons of these two coffee blends each day. Pomona is a blend of 20% Colombian, 35% Kenyan, and 45% Indonesian, while Coastal is a blend of 60% Colombian, 10% Kenyan, and 30% Indonesian. The shop sells 1.5 times more Pomona than Coastal each day. Pomona sells for $2.05 per cup, and Coastal sells for $1.85 per cup. The manager wants to know how many cups of each blend to sell each day in order to maximize sales. The problem is modelled below and solved (therefore, you will not model the problem) and the following sensitivity analysis report is the output. Max 2.05*x1 +1.85*x2 s.t. x1+x2 s 250.5 X1 - 1.5*2=0 0.0125*x1 +0.0375*X2 56 0.021875*x1 +0.006250x256 0.028125x1 +0.01875*X2 56 X1, X20 Variable Cells Cell $B$8 $B$9 Name Pomona Coastal Final Value 147.7 98.5 Reduced Cost 0 0 Objective Coefficient 2.05 1.85 Allowable Increase 15:30 1E30 Allowable Decrease 33 49 Constraints Cell Name $D$15 Brew Cap SD$16 Demand SD$17 Colombian $D$18 Kenyan SD$19 Indonesian Final Value 246.2 0 5.5 3.8 6 Shadow Price 2 -0.2 0 0 80.8 Constraint R.H. Side 250.5 0 6 6 6 Allowable Increase 1E+30 213.3 15-30 15:30 0.1 Allowable Decrease 43 28.3 0.5 22 6 Answer the following questions a) (8 points) What is the current optimal solution? Calculate the optimal profit. b) (8 points) For which values of the profit per cup of Pomona current optimal solution remains optimal? c) (8 points) You have found a new small supplier of Indonesian coffee. The new supplier offers to sell 0.05 pounds. Can you calculate the effect of this change to the objective function? If your answer is yes, what is the change in the optimal value? If your answer is no, why cannot you calculate? d) (8 points) You have just realized that your supplier actually can provide 5 pounds of Colombian Can you calculate the effect of this change to the objective function? if your answer is yes, what is the change in the optimal value? If your answer is no why cannot you calculate? e) (8 points) What should be the shadow price of brew capacity constraint it is not given in the table)? Explain your
