A factory produces two products A and B. In the manufacturing of product A, the machine and the carpenter requires 3 hour each and in manufacturing of product B, the machine and carpenter requires 5 hour and 3 hour respectively. The machine and carpenter work at most 80 hour and 50 hour per week respectively. The profit on A and B is Rs. 6 and 8 respectively. If profit is maximum by manufacturing x and y units of A and B type product respectively, then for the funcxtion 6x + 8y the constraints are

Question

A factory produces two products A and B. In the manufacturing of product A, the machine and the carpenter requires 3 hour each and in manufacturing of product B, the machine and carpenter requires 5 hour and 3 hour respectively. The machine and carpenter work at most 80 hour and 50 hour per week respectively. The profit on A and B is Rs. 6 and 8 respectively. If profit is maximum by manufacturing x and y units of A and B type product respectively, then for the funcxtion 6x + 8y the constraints are (A) x ≥ 0, y ≥ 0, 5x + 3y ≤ 80, 3x + 2y ≤ 50  (B) x ≥ 0, y ≥ 0, 3x + 5y ≤ 80, 3x + 2y ≤ 50  (C) x ≥ 0, y ≥ 0, 3x + 5y ≤ 80, 2x + 3y ≥ 50  (D) x ≥ 0, y ≥ 0, 5x + 3y ≥ 80, 3x + 2y ≥ 50

Tardigrade Admin · Accepted Answer

Obviously x, y ≥ 0, 3x + 5y ≤ 80, 3x + 3y ≤ 50.

$x \geq 0, y \geq 0, 5 x + 3 y \leq 80, 3 x + 2 y \leq 50$

$x \geq 0, y \geq 0, 3 x + 5 y \leq 80, 3 x + 2 y \leq 50$

$x \geq 0, y \geq 0, 3 x + 5 y \leq 80, 2 x + 3 y \geq 50$

$x \geq 0, y \geq 0, 5 x + 3 y \geq 80, 3 x + 2 y \geq 50$

Obviously $x, y \geq 0, 3 x + 5 y \leq 80, 3 x + 3 y \leq 50.$

x≥0,y≥0,5x+3y≤80,3x+2y≤50

x≥0,y≥0,3x+5y≤80,3x+2y≤50

x≥0,y≥0,3x+5y≤80,2x+3y≥50

x≥0,y≥0,5x+3y≥80,3x+2y≥50

Obviously x,y≥0,3x+5y≤80,3x+3y≤50.

$x \geq 0, y \geq 0, 5 x + 3 y \leq 80, 3 x + 2 y \leq 50$

$x \geq 0, y \geq 0, 3 x + 5 y \leq 80, 3 x + 2 y \leq 50$

$x \geq 0, y \geq 0, 3 x + 5 y \leq 80, 2 x + 3 y \geq 50$

$x \geq 0, y \geq 0, 5 x + 3 y \geq 80, 3 x + 2 y \geq 50$

Obviously $x, y \geq 0, 3 x + 5 y \leq 80, 3 x + 3 y \leq 50.$