$[30$ points$]$ 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. Profit from Fan A is $$35,$ Fan B profit is $$50,$ and Fan C profit is $$60.$ TriStar Manufacturing wants to know the best product mix to maximize the revenue.

$\backslash$table$[[,$Fan A$,$Fan B$,$Fan C$,],[$Component$,$# Needed,# Needed,# Needed,Current Inventory$],[$Wire$,5,6,10,8000],[$Nuts$,8,7,15,12000],[$Bolts$,8,10,12,10000],[$Motor$,1,1,1,1500],[$Blades$,3,5,5,7500]]$

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. If you used Excel Solver, a screen capture of the Solver parameters must be shown to earn full credit.

d$.$ How much profit does the manufacturer earn with optimal production quantitioc?