Plz help Four products are produced on three machines The ma

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 the amount of Product A produced by machine 1 be A₁, by machine 2 be A₂ and so on.

Similarly for Product B, C and D, let it be B₁, B₂, B₃, C₁, C₂ and so on.

Maximise Profit = 18*(A₁ + A₂ + A₃) + 25*(B₁ + B₂ + B₃) + 10*(C₁ + C₂ + C₃) + 15*(D₁ + D₂ + D₃)

Subject to:

1.2*A₁ + 1.3*B₁ + 0.7*C₁ + 0*D₁ = 2000

0.7*A₂ + 2.2*B₂ + 1.6*C₂ + 0.5*D₂ = 2500

1.4*A₃ + 2.8*B₃ + 1.3*C₃ + 1.2*D₃ = 3400