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
Answer & explanation
Correct answer: option 1
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)
|
Labour hours required |
||
|
|
Fabricating |
Finishing |
|
$M_1$ |
9 |
1 |
|
$M_2$ |
12 |
3 |
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)