Billy D. is a manager for musical groups. Billy is working on marketing material and has been presented with the following information about two different products that can be used for printing. The box with T-shirts (T) is less expensive to buy and costs $15.00. The box of caps costs $22.00. Billy's boss asks him how many boxes should they buy of each product to MINIMIZE the costs, subject to the following constraints such as hours:

MIN 15T + 22C

s.t. 8T + 4C 200

2T + 7C 180

10T 150

6C 120

T,C 0

b. Use a graph to show each constraint and the feasible region.

c. Identify the optimal solution point on your graph.

d. How many boxes of T-shirts should they purchase to minimize the cost & how much will cost?

e. How many boxes of caps should they purchase to minimize the cost & how much will cost?

f. What is the optimal objective value of the objective function (dollar value)?

g. Which constraints are binding?

h. What is the dual value for constraint 3? Interpret the dual value.

i. If Billy's manager tells him the next day that they actually can increase the value of constraint 3 to 200, what would change? Why?

j. What is the range of optimality for T-Shirts and caps?

Please show steps in excel with any formulas used.