Use Linear Programming to Solve Problems
-Objective Function
$$\begin{array} { l }
z = 5 x + 7 y \
x \geq 0 \
0 \leq y \leq 5 \
2 x + 3 y \geq 12 \
2 x + 3 y \leq 20
\end{array}$$
$$\text { Constraints } \quad x \geq 0$$
A) Maximum: 50; at $( 10,0 )$
B) Maximum: 45 ; at $( 2,5 )$
C) Maximum: 30 ; at $( 6,0 )$
D) Maximum: $- 20$; at $( 4,0 )$

Question

Use Linear Programming to Solve Problems
-Objective Function
$$\begin{array} { l } 
z = 5 x + 7 y \
x \geq 0 \
0 \leq y \leq 5 \
2 x + 3 y \geq 12 \
2 x + 3 y \leq 20
\end{array}$$
$$\text { Constraints } \quad x \geq 0$$
A) Maximum: 50; at $( 10,0 )$
B) Maximum: 45 ; at $( 2,5 )$
C) Maximum: 30 ; at $( 6,0 )$
D) Maximum: $- 20$; at $( 4,0 )$

Quizplus · Accepted Answer

The objective function is maximized at the corner point where the two constraints intersect. The corner points are $( 0,0 ), ( 0,5 ), ( 6,0 ), and ( 2,5 )$. The objective function value at these points are 0, 35, 30, and 45, respectively. Therefore, the maximum value of the objective function is 45, which occurs at the point $( 2,5 )$.

Use Linear Programming to Solve Problems -Objective Function z=5x+7yx≥00≤y≤52x+3y≥122x+3y≤20\begin{array} { l } z = 5 x + 7 y \\x \geq 0 \\0 \leq y \leq 5 \\2 x + 3 y \geq 12 \\2 x + 3 y \leq 20\end{array}z=5x+7yx≥00≤y≤52x+3y≥122x+3y≤20​

Use Linear Programming to Solve Problems
-Objective Function $\begin{array} { l } z = 5 x + 7 y \\x \geq 0 \\0 \leq y \leq 5 \\2 x + 3 y \geq 12 \\2 x + 3 y \leq 20\end{array}$