Solve the linear programming problem. Minimize $C = - 2 x - 5 y$ subject to $$\begin{array} { l }
3 x + 5 y \leq 10 \
7 x - 6 y \leq 18 \
x \geq 0 , y \geq 0
\end{array}$$
A) $x = 1$ , $y = 1$ , $C = - 7$
B) $x = 2$ , $y = 2$ , $C = - 14$
C) $x = 0$ , $y = 2$ , $C = - 10$
D) $x = 2$ , $y = 0$ , $C = - 4$
E) $x = 1$ , $y = 2$ , $C = - 12$

Question

Solve the linear programming problem. Minimize $C = - 2 x - 5 y$ subject to $$\begin{array} { l } 
3 x + 5 y \leq 10 \
7 x - 6 y \leq 18 \
x \geq 0 , y \geq 0
\end{array}$$  
A) $x = 1$ , $y = 1$ , $C = - 7$
B) $x = 2$ , $y = 2$ , $C = - 14$
C) $x = 0$ , $y = 2$ , $C = - 10$
D) $x = 2$ , $y = 0$ , $C = - 4$
E) $x = 1$ , $y = 2$ , $C = - 12$

Quizplus · Accepted Answer

To solve this linear programming problem, we graph the constraints and find the feasible region. The objective function $C = -2x - 5y$ needs to be minimized. By evaluating $C$ at the vertices of the feasible region, we find that the minimum value of $C$ occurs at $x = 0$, $y = 2$, which gives $C = -10$.

Solve the Linear Programming Problem C=−2x−5yC = - 2 x - 5 yC=−2x−5y

Solve the Linear Programming Problem $C = - 2 x - 5 y$