Use Linear Programming to Solve Problems
-Objective Function $\quad \mathrm { z } = 24 \mathrm { x } + 21 \mathrm { y }$
Constraints
$$\begin{array} { l }
0 \leq x \leq 10 \
0 \leq y \leq 5 \
3 x + 2 y \geq 6
\end{array}$$
A) Maximum: 345; at $( 10,5 )$
B) Maximum: 240; at $( 10,0 )$
C) Maximum: 105 ; at $( 0,5 )$
D) Maximum: 63 ; at $( 0,3 )$

Question

Use Linear Programming to Solve Problems
-Objective Function $\quad \mathrm { z } = 24 \mathrm { x } + 21 \mathrm { y }$
Constraints
$$\begin{array} { l } 
0 \leq x \leq 10 \
0 \leq y \leq 5 \
3 x + 2 y \geq 6
\end{array}$$
A) Maximum: 345; at $( 10,5 )$
B) Maximum: 240; at $( 10,0 )$
C) Maximum: 105 ; at $( 0,5 )$
D) Maximum: 63 ; at $( 0,3 )$

Quizplus · Accepted Answer

The maximum value of the objective function $z = 24x + 21y$ occurs at the corner point of the feasible region defined by the constraints. The constraints define a rectangle in the first quadrant bounded by $x = 10$ and $y = 5$, with an additional constraint $3x + 2y \geq 6$ which does not further restrict the maximum since the corner point $(10, 5)$ already satisfies this inequality. Substituting $x = 10$ and $y = 5$ into the objective function gives $z = 24(10) + 21(5) = 240 + 105 = 345$, indicating the maximum value is achieved at this point.

Use Linear Programming to Solve Problems -Objective Function z=24x+21y\quad \mathrm { z } = 24 \mathrm { x } + 21 \mathrm { y }z=24x+21y

Use Linear Programming to Solve Problems
-Objective Function $\quad \mathrm { z } = 24 \mathrm { x } + 21 \mathrm { y }$