Question

Consider the linear programming problem: Maximise $z=4x+y$ Subject to constraints $x+y\le 50,x+y\ge 100$ and $x,y\ge 0$. Then, the maximum value of $z$ is

• A. $0$
• B. $50$
• C. $100$
• D. None of these

Answer 1

The correct option is D

None of these

Explanation for the correct options:

Option (4) None of these

Maximize $Z=4x+y$

Subjected to the constrains

$$\begin{gathered} x+y\le 50 \\ x+y\ge 100 \\ x,y\ge 0 \end{gathered}$$

Region represented by $x+y\le 50$

x	0	50
y	50	0

The line $x+y=50$ meets the coordinate axis at $\left(0,50\right)$ and $\left(50,0\right)$

Region represented by $x+y\ge 100$

x	0	100
y	100	0

The line $x+y=100$ meets the coordinate axis at $\left(0,100\right)$ and $\left(100,0\right)$

Plot the graph using the data

There is no common region. Therefore there is no solution

Therefore, option (4) is the correct answer