The Fair Lady Hat Company produces three distinct styles of hat. The operations manager has modeled the operations using linear programming. She is using x1, x2, and x3 to represent each hat style. Below is her formulation: MaximizeZ=270x1 +345x2 +265x3 Subject to: Machine A: Machine B: MachineC: 2 x1 + 3 x2 + 2 x3 < 220 hours 5 x1 + 2 x2 + 1 x3 < 350 hours 3x1 +2x2 +4x3 <190hours x1>0; x2 >0; x3 >0 ??????a. Use Excel and Solver to find the optimal solution for this problem. What is the value of the objective function? What are the optimal values of the product mix? Attach the printouts of worksheets for the final solution and the sensitivity report. Then consider the statements below independently and explain each of your answers. b. If the marginal price of Hat 3 were to increase by $25, would she have to make changes to the values of the product mix? c. Suppose the capacity of Machine B were to be reduced to 260 hours, would that have any impact on total profits? d. If machine C had a capacity of 155 hours instead of its current value of 190, how would the Total Profit be impacted?