The maximum value of P = 6x + 8y subject to constraints 2x + y ≤ 30 , x + 2y ≤ 24 and x ≥ 0 , y ≥ 0 is

Question

The maximum value of P = 6x + 8y subject to constraints 2x + y ≤ 30 , x + 2y ≤ 24 and x ≥ 0 , y ≥ 0 is (A) 90 (B) 120 (C) 96 (D) 240

Tardigrade Admin · Accepted Answer

Here , 2x + y ≤ 30, x + 2y ≤ 24 , x , y ≥ 0 The shaded region represents the feasible region, hence P = 6x + 8y. Obviously it is maximum at (12, 6). Hence, P = 12 × 6 + 8 × 6 = 120

Q. The maximum value of $P = 6 x + 8 y$ subject to constraints $2 x + y \leq 30, x + 2 y \leq 24$ and $x \geq 0, y \geq 0$ is

90

120

96

240

Here , $2 x + y \leq 30, x + 2 y \leq 24, x, y \geq 0$
The shaded region represents the feasible region, hence $P = 6 x + 8 y$ . Obviously it is maximum at (12, 6).
Hence, $P = 12 \times 6 + 8 \times 6 = 120$

Q. The maximum value of P=6x+8y subject to constraints 2x+y≤30,x+2y≤24 and x≥0,y≥0 is

90

120

96

240

Here , 2x+y≤30,x+2y≤24,x,y≥0 The shaded region represents the feasible region, hence P=6x+8y. Obviously it is maximum at (12, 6). Hence, P=12×6+8×6=120

Q. The maximum value of $P = 6 x + 8 y$ subject to constraints $2 x + y \leq 30, x + 2 y \leq 24$ and $x \geq 0, y \geq 0$ is

Here , $2 x + y \leq 30, x + 2 y \leq 24, x, y \geq 0$
The shaded region represents the feasible region, hence $P = 6 x + 8 y$ . Obviously it is maximum at (12, 6).
Hence, $P = 12 \times 6 + 8 \times 6 = 120$