A manufacturing company makes two models $M_1$ and $M_2$ of a product. Each piece of $M_1$ requires 9 labour hours for fabricating and one labour hour for finishing. Each piece of $M_2$ require 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs. 800 on each piece of $M_1$ and Rs. 1200 on each piece of $M_2$

The above Linear Programming Problem [LPP] is given by

Maximize $Z=800 x+1200 y$

Subject to constraints,

$3 x+4 y \leq 60$

$x+3 y \leq 30$

$x, y \geq 0$

Profit on $M_1$ = 800 / piece

$M_2$ = 1200 / piece

let pieces of M₁ be x and M₂ be y

so function → Maximise Z = 800x + 1200y (profit needs to be maximised)

Maximum available hours for fabrication = 180

finishing = 30

so 9x +12y ≤ 180

⇒ 3x + 4y ≤ 60

x + 3y ≤ 30

x, y ≥ 0 (atleast some no products needs to be formed hence it can't be zero)