The Charm City Fan Company manufactures two products: large fans and medium fans
ID: 3107442 • Letter: T
Question
The Charm City Fan Company manufactures two products: large fans and medium fans. Each large fan requires 3 hours of wiring and 2 hours of drilling. Each medium fan requires 2 hours of wiring and 1 hour of drilling. There are 480 hours of wiring time available and 280 hours of drilling time available. Each large fan yields a profit of $15. Each medium fan yields a profit of $10. The company wants to manufacture at least 40 large fans.
(a) Formulate a linear programming model to maximize total profit for this problem.
(b) Find the optimal solution of this model by hand using the corner points graphical method.
Explanation / Answer
let x be the number of large fans and y be the number of medium fans 3x + 2y = 480 2x + 1y = 280 3x + 2(280 - 2x) = 480 3x + 560 - 4x = 480 x = 80 y = 280 - 2(80) = 120 profit: 80 * 15 + 120 * 10 = $2400