Minimize $c = 50 x + 11 y + 50 z$
Subject to
$$\begin{array} { r }
3 x + z \geq 6 \
3 x + y - z \geq 6 \
4 x + y - z \leq 8 \
x \geq 0 , y \geq 0 , z \geq 0
\end{array}$$
A) $c = 400$ , $x = 8$ , $y = 0$ , $z = 0$
B) $c = 716$ , $x = 8$ , $y = 6$ , $z = 5$
C) $c = 88$ , $x = 0$ , $y = 0$ , $z = 8$
D) $c = 100$ , $x = 2$ , $y = 0$ , $z = 0$
E) no solution

Question

Minimize   $c = 50 x + 11 y + 50 z$ 
Subject to
  $$\begin{array} { r } 
3 x + z \geq 6 \
3 x + y - z \geq 6 \
4 x + y - z \leq 8 \
x \geq 0 , y \geq 0 , z \geq 0
\end{array}$$  
A) $c = 400$ , $x = 8$ , $y = 0$ , $z = 0$
B) $c = 716$ , $x = 8$ , $y = 6$ , $z = 5$
C) $c = 88$ , $x = 0$ , $y = 0$ , $z = 8$
D) $c = 100$ , $x = 2$ , $y = 0$ , $z = 0$
E) no solution

Quizplus · Accepted Answer

The constraints can be satisfied with $x = 2$, $y = 0$, and $z = 0$, leading to the minimum cost $c = 100$.

Minimize c=50x+11y+50zc = 50 x + 11 y + 50 zc=50x+11y+50z

Minimize $c = 50 x + 11 y + 50 z$