TriStar Manufacturing makes three models of fans, identified by the unimaginative names of A, B, and C. The fans are made out of nuts, bolts, wire, blades, and motors. The current inventory levels and parts list for each type of fan is shown in the table below. Fan A sells for $18, Fan B sells for $25, and Fan C sells for $30. Fan A Fan B Fan C Component # Needed # Needed # Needed Current Inventory Wire 1 2 3 500 Nuts 8 12 14 700 Bolts 8 12 14 700 Motor 1 1 2 200 Blades 5 6 7 400 a. What are decision variables for this problem? What is the objective function for this problem? b. What are the constraints for this problem? Express them as mathematical relationships. C. Solve the problem using Excel Solver or LP Solve. How many of each type to make so as to maximize profits? Show screen captures to earn full credit. d. How much profit the manufacturer earns with optimal production quantities