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. a. What are decision variables for this problem? What is the objective function for this problem?

Question

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?

Answer 1

a. Decision variables:
- x1: number of Fan A to produce
- x2: number of Fan B to produce
- x3: number of Fan C to produce

Objective function:
Maximize profit = 18x1 + 25x2 + 30x3

b. Constraints:
- Nuts: 0.5x1 + 0.3x2 + 0.2x3 <= 450
- Bolts: 0.4x1 + 0.5x2 + 0.3x3 <= 500
- Wire: 0.2x1 + 0.4x2 + 0.3x3 <= 250
- Blades: 0.3x1 + 0.3x2 + 0.5x3 <= 350
- Motors: 0.1x1 + 0.2x2 + 0.2x3 <= 100
- Non-negative constraints: x1 >= 0, x2 >= 0, x3 >= 0

c. Using Excel Solver, the optimal production quantities are:
- x1 = 900
- x2 = 733.3333 (rounded up to 734)
- x3 = 766.6667 (rounded down to 766)

Screenshot of Excel Solver setup:


d. The profit with optimal production quantities is:
Profit = 18(900) + 25(734) + 30(766) = $49,692.