Question

Solve the linear programming problem: max $Z=x+2y$ subject to constraints: $x-y\le 10,$ $2x+3y\le 20,$ $x\le 0,y\le 0$

• A. $Max.Z=10$
• B. $Max.Z=30$
• C. $Max.Z=40$
• D. $Max.Z=50$
• E. None of these

Answer 1

Answer: (E)

We have, max $Z=x+2y$ Subject to constraints, $x-y\le 10$ $2x+3y\le 20$ $x\ge 0,y\ge 0$ On taking given constraints as equation, we get The following graph.
Here, OAB is the required feasible region whose comer points are $O(0,0),A(10,0)$ and $B\left(0,\frac{20}{3}\right)$ .
Comer point
$z=x+2y$
at $O(0,0)$
$Z=0$
at $A(10,0)$
$Z=10$
at $B\left(0,\frac{20}{3}\right)$
$Z=0+2\times \frac{20}{3}=\frac{40}{3}$
Hence, maximum value of Z is $\frac{40}{3},$ which is obtained at $B\left(0,\frac{20}{3}\right).$