Maximize $p = 2 x + 3 y + z + 4 w$
Subject to
$\begin{aligned}
x + y + z + w & \leq 40 \
2 x + y - z - w & \geq 10 \
x + y + z + w & \geq 10 \
x \geq 0 , y \geq 0 , z \geq 0 , w & \geq 0
\end{aligned}$

A) $p = 65$ , $x = 25$ , $y = 0$ , $z = 15$ , $w = 0$
B) $p = 135$ , $x = 0$ , $y = 25$ , $z = 0$ , $w = 15$
C) $p = 130$ , $x = 0$ , $y = 15$ , $z = 0$ , $w = 15$
D) $p = 55$ , $x = 15$ , $y = 0$ , $z = 25$ , $w = 0$
E) no solution

Question

Maximize  $p = 2 x + 3 y + z + 4 w$  
Subject to
  $\begin{aligned}
x + y + z + w & \leq 40 \
2 x + y - z - w & \geq 10 \
x + y + z + w & \geq 10 \
x \geq 0 , y \geq 0 , z \geq 0 , w & \geq 0
\end{aligned}$

A) $p = 65$ , $x = 25$ , $y = 0$ , $z = 15$ , $w = 0$
B)   $p = 135$ , $x = 0$ , $y = 25$ , $z = 0$ , $w = 15$
C)   $p = 130$ , $x = 0$ , $y = 15$ , $z = 0$ , $w = 15$
D)    $p = 55$ , $x = 15$ , $y = 0$ , $z = 25$ , $w = 0$
E) no solution

Quizplus · Accepted Answer

The solution satisfies all constraints and maximizes the objective function $p = 2x + 3y + z + 4w$.

Maximize p=2x+3y+z+4wp = 2 x + 3 y + z + 4 wp=2x+3y+z+4w

Maximize $p = 2 x + 3 y + z + 4 w$