Find the maximum value of the objective function and where it occurs, if one exists. Objective function: $z = 2 x - 4 y$ Constraints: $\begin{aligned}
x & \geq 0 \
y & \geq 0 \
- x + y & \leq 1 \
- 5 x + y & \geq 5
\end{aligned}$
A)The solution region is empty. There is no maximum value.
B)The maximum value is 2 and occurs at $( 1,0 )$
C)The maximum value is -4 and occurs at $( 0,1 )$
D)The maximum value is -20 and occurs at $( 0,5 )$
E)The maximum value is 10 and occurs at $( 5,0 )$

Question

Quizplus · Accepted Answer

The constraints $-x + y \leq 1$ and $-5x + y \geq 5$ form a system of inequalities that do not have a common solution area when combined with $x \geq 0$ and $y \geq 0$. This is because the second inequality implies a region that is below a line with a much steeper slope than the line defined by the first inequality, making it impossible for both conditions to be satisfied simultaneously in the first quadrant (where $x \geq 0$ and $y \geq 0$). Therefore, there is no solution region where these constraints overlap, meaning there is no maximum value for the objective function under these conditions.

Find the Maximum Value of the Objective Function and Where z=2x−4yz = 2 x - 4 yz=2x−4y

Find the Maximum Value of the Objective Function and Where $z = 2 x - 4 y$