Find the value(s) of the function, subject to the system of inequalities.
-Find the maximum and minimum of $z = 18 x + 24 y$ subject to $x \geq 0 , y \geq 0,4 x + 5 y \leq 30,4 x + 3 y \leq 20 , x \leq 5 , y \leq 8$
A) $- 144 ; 0$
B) $- 97.5 ; - 144$
C) $90 ; 0$
D) $90 ; - 144$

Question

Quizplus · Accepted Answer

To find the maximum and minimum values of $z = 18x + 24y$ subject to the given constraints, we graph the inequalities and identify the feasible region. The vertices of the feasible region, found by intersecting the lines of the inequalities, are key points to evaluate. The constraints are $x \geq 0$, $y \geq 0$, $4x + 5y \leq 30$, $4x + 3y \leq 20$, $x \leq 5$, and $y \leq 8$. Evaluating $z$ at these vertices gives the maximum and minimum values of $z$ within the feasible region. The maximum value of $z$ is found to be 90, and the minimum value is -144, making option D correct.

Find the Value(s) of the Function, Subject to the System z=18x+24yz = 18 x + 24 yz=18x+24y

Find the Value(s) of the Function, Subject to the System $z = 18 x + 24 y$