Minimize $c = 4 x + 7 y$
Subject to
$\begin{array} { l }
8 x + 3 y \geq 30 \
2 x + 3 y \geq 12 \
x \geq 0 , y \geq 0
\end{array}$
A) $c = 24$ , $x = 6$ , $y = 0$
B) $c = 21$ , $x = 0$ , $y = 3$
C) $c = 6$ , $x = 3$ , $y = 0$
D) $c = 42$ , $x = 0$ , $y = 6$
E) no solution

Question

Minimize  $c = 4 x + 7 y$  
Subject to
  $\begin{array} { l } 
8 x + 3 y \geq 30 \
2 x + 3 y \geq 12 \
x \geq 0 , y \geq 0
\end{array}$  
A) $c = 24$ , $x = 6$ , $y = 0$
B) $c = 21$ , $x = 0$ , $y = 3$
C) $c = 6$ , $x = 3$ , $y = 0$
D) $c = 42$ , $x = 0$ , $y = 6$
E) no solution

Quizplus · Accepted Answer

To minimize $c = 4x + 7y$, we can graph the constraints and find the feasible region. The optimal solution (minimum c) occurs at a vertex of the feasible region. Testing the vertices (which are the intersections of the constraints) against the objective function, we find that $x = 6, y = 0$ gives the minimum value of $c = 24$.

Minimize c=4x+7yc = 4 x + 7 yc=4x+7y Subject To 8x+3y≥302x+3y≥12x≥0,y≥0\begin{array} { l } 8 x + 3 y \geq 30 \\2 x + 3 y \geq 12 \\x \geq 0 , y \geq 0\end{array}8x+3y≥302x+3y≥12x≥0,y≥0​

Minimize $c = 4 x + 7 y$ Subject To $\begin{array} { l } 8 x + 3 y \geq 30 \\2 x + 3 y \geq 12 \\x \geq 0 , y \geq 0\end{array}$