Minimize $p = 6 a + 4 b$ subject to the following constraints.
$\begin{array} { l }
a + b \geq 10 \
6 a + b \geq 30 \
a \geq 0 , b \geq 0
\end{array}$
A) $a = 4$ , $b = 6$ , $p = 48$
B) $a = 10$ , $b = 0$ , $p = 60$
C) $a = 0$ , $b = 30$ , $p = 180$
D) $a = 0$ , $b = 10$ , $p = 40$
E) $a = 6$ , $b = 6$ , $p = 60$

Question

Minimize $p = 6 a + 4 b$ subject to the following constraints.  
  $\begin{array} { l } 
a + b \geq 10 \
6 a + b \geq 30 \
a \geq 0 , b \geq 0
\end{array}$  
A) $a = 4$ , $b = 6$ , $p = 48$
B)   $a = 10$ , $b = 0$ , $p = 60$
C) $a = 0$ , $b = 30$ , $p = 180$
D) $a = 0$ , $b = 10$ , $p = 40$
E) $a = 6$ , $b = 6$ , $p = 60$

Quizplus · Accepted Answer

To minimize $p = 6a + 4b$, we graph the constraints and find the feasible region. The optimal solution occurs at a vertex of the feasible region. Testing the vertices given in the options, only $a = 4, b = 6$ satisfies all constraints and gives the minimum $p = 48$.

Minimize p=6a+4bp = 6 a + 4 bp=6a+4b Subject to the Following Constraints

Minimize $p = 6 a + 4 b$ Subject to the Following Constraints