Mainly PART D, E, F, G

The Bottom Line Coffee House in Midtown, Detroit serves two coffee blends it brews on a daily basis, House Blend and Major Dickason's Blend. Each is a blend of three high-quality coffees from Colombia, Kenya, and Indonesia. The coffee shop has 7.5, 10, and 15 pounds of Colombia, Kenya, and Indonesia coffees available each day, respectively. Each pound of coffee will produce sixteen 16-ounce cups of coffee. The shop has enough brewing capacity to brew 60 gallons of these two coffee blends each day. House is a blend of 20% Colombian, 20% Kenyan, and 60% Indonesian, while Major Dickason's is a blend of 25% Colombian, 50% Kenyan, and 25% Indonesian. The shop sells more House than Major Dickason's each day, so they want to produce more House than Major Dickason's. House sells for $1.50 per cup, and Major Dickason's sells for $2.00 per cup. The manager wants to know how many cups of each blend to sell each day in order to maximize sales. a. [5 points] Formulate a linear programming model for this problem. b. (5 points) Solve this model by using graphical analysis. Draw at least three objective function lines to determine the optimal solution (Hint: Use the method 1 for finding the optimal solution as discussed in the lectures). c. (5 points] Give the coordinates of all extreme points. Calculate the profit at the extreme points and validate the solution you found in part b (Hint: Use the method 2 for finding the optimal solution as discussed in the lectures). d. (5 points) Identify the range for the profit from a cup of House Blend that will keep the solution in (b) optimal using sensitivity analysis. (Hint: The coefficient of the House Blend variable in the objective function] e. [5 points) Determine the sensitivity range for the brewing capacity using sensitivity analysis. (Hint: Change in the available resource for brewing capacity] f. (5 points] Determine the sensitivity range for the coffee from Kenya using sensitivity analysis. (Hint: Change in the available resource for the coffee from Kenya] g. (5 points] Determine the sensitivity range for the coffee from Indonesia using sensitivity analysis. (Hint: Change in the available resource for the coffee from Indonesia)