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 $12. Each medium fan yields a profit of $8. The company wants to manufacture 160 or fewer medium 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.