Find the value(s) of the function, subject to the system of inequalities.
-Find the maximum and minimum of $$z = 19 x + 7 y \text { subject to } x \geq 0 , y \geq 0,2 x + 3 y \geq 6 , x \leq 10 , y \leq 5$$
A) 35; 21
B) 225; 14
C) 190; 21
D) 225; 190

Question

Quizplus · Accepted Answer

To find the maximum and minimum values of $z = 19x + 7y$ subject to the given constraints, we need to evaluate $z$ at the vertices of the feasible region defined by the inequalities. The constraints are $x \geq 0$, $y \geq 0$, $2x + 3y \geq 6$, $x \leq 10$, and $y \leq 5$.1. Intersection of $x = 0$ and $2x + 3y = 6$ gives $y = 2$.2. Intersection of $y = 0$ and $2x + 3y = 6$ gives $x = 3$.3. The points $(10, 0)$ and $(0, 5)$ are vertices due to the constraints $x \leq 10$ and $y \leq 5$.4. Intersection of $x = 10$ and $2x + 3y = 6$ does not provide a feasible solution within the given constraints.5. Intersection of $y = 5$ and $2x + 3y = 6$ does not provide a feasible solution within the given constraints.Evaluating $z$ at the vertices:- At $(0, 2)$, $z = 19(0) + 7(2) = 14$.- At $(3, 0)$, $z = 19(3) + 7(0) = 57$.- At $(10, 0)$, $z = 19(10) + 7(0) = 190$.- At $(0, 5)$, $z = 19(0) + 7(5) = 35$.The maximum value of $z$ is 190, and the minimum value is 14, which corresponds to choice B.

Find the Value(s) of the Function, Subject to the System z=19x+7y subject to x≥0,y≥0,2x+3y≥6,x≤10,y≤5z = 19 x + 7 y \text { subject to } x \geq 0 , y \geq 0,2 x + 3 y \geq 6 , x \leq 10 , y \leq 5z=19x+7y subject to x≥0,y≥0,2x+3y≥6,x≤10,y≤5

Find the Value(s) of the Function, Subject to the System $z = 19 x + 7 y \text { subject to } x \geq 0 , y \geq 0,2 x + 3 y \geq 6 , x \leq 10 , y \leq 5$