Question

A 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 $25. Each medium fan yields a profit of $18. The company wants to manufacture at least 20 large fans. The objective is to maximize total profit.

(a) Formulate a linear optimization model for this problem by defining the decision variables, objective function and all the constraints. What do they represent?

(b) Find the optimal solution of this model by hand using the Corner Points graphical method.

Answer 1

objective function to maximise the total profit

Max (25x+18y), where x is the number of large fans made and y is the number of small fans made.

3x+2y<=480

2x+y<280

x=>0, y=>0

Points of optimality are ( 140,0) ( 0,240) and (80,120)

Value of objective function at different points

at (140,0) = 140x25 +0 =3500

at (0,240) =18x240 =4320

at (80,120) = 25x80+18x120 =4160

(0,240) is the optimum soution, i.e. to produce 240 small fans