Four products are produced on three machines The machine req

Four products are produced on three machines. The machine requirements per unit of product, the profit per unit of product, and the time available on each machine are shown in the table below. Set up the linear programming model to maximize profit. (Stating the problem is sufficient; you do not have to introduce variables or set up the tableau.)

Solution

Let x, y, z and t units of product A, B, C and D are produced using three machines. The objective is to maximize profit (P). Hence, the objective function is Maximize P = 18x + 25y + 10z + 15t

The machine requirements per unit of product are given in the table. The available time for machine 1, 2, and 3 are 2000, 2500, and 3400 respectively. Hence, for machine 1, the constraint inequality is 1.2x + 1.3y + 0.7z + 0.0t 2000

For machine 2, the constraint inequality is 0.7x + 2.2y + 1.6z + 0.5t 2500

For machine 3, the constraint inequality is 1.4x + 2.8y + 1.3z + 1.2t 3400

The non-negativity restrictions are given by x, y, z, t 0 (as the units of production cannot be negative)

Therefore the Linear Programming model is

Maximize P = 18x + 25y + 10z + 15t

Subject To, 1.2x + 1.3y + 0.7z 2000

0.7x + 2.2y + 1.6z + 0.5t 2500

1.4x + 2.8y + 1.3z + 1.2t 3400

x, y, z, t 0 (Answer)