Question

We need to assemble two models of six-leg tables. The basic version has a wood top and requires 0.6 hours to assemble. The profit is $200 for each table. The deluxe version has a glass top and requires 1.5 hours to assemble. The profit is $350 for each table. In the next week, 300 legs, 50 wood tops, 35 glass tops and 63 hours of assembly are available. Please formulate an LP model to maximize total profit assuming everything produced can be sold. Please solve the model graphically X. 1. Table 0.6hp/n 200/26 1 4 legs wood Top

Answer 1

Let

Number of basic version = X

Number of deluxe version = Y

Formulation

Maximize 200X + 350Y

Subject to

0.6X + 1.5Y <= 63

6X + 6Y <= 300

X <= 50

Y <= 35

X, Y >= 0

The constraints are drawn on the graph shown below. The corner points are marked as well

(0.35) (15, 35) 304 (50, 0) | (50, 0) -10 ||||| 10 30 40 60 | | 70 190 100 110 | | 130 140

The objective function values are

(0,35) = 35*350 = 12250

(15,35) = 15*200 + 35*350 = 15250

(50,0) = 50*200 = 10000

The optimal solution is 15 wood top and 35 glass top tables