Question

Maximize $Z=4x+9y$, subject to the constralnts $x=0$, y $=0,x+5y\le 200,2x+3y\le 134$.

• (A) 359
• (B) 856
• (C) 382
• (D) 756

Answer 1

The Correct Option is C

Explanation:
Given:$Z=4x+9y$, subject to the constralnts $x=0$, y $=0,x+5y\le 200,2x+3y\le 134$.

The corner points of feasible region are $\mathrm{A}(10,38),\mathrm{B}(0,40),\mathrm{C}(0,0),\mathrm{D}(67,0)$.The values of $Z$ at the following polnts is$\begin{array}{|lll|}\hline \text{Corner Point}& \mathrm{Z}=4\mathrm{x}+9\mathrm{y}& \\ \mathrm{A}(10,38)& 382& \text{Maximum}\\ \mathrm{B}(0,40)& 360& \\ \mathrm{C}(0,0)& 0& \\ \mathrm{D}(67,0)& 268& \\ \hline\end{array}$The maxlmum value of $Z$ Is 382 at polnt $A(10,38)$.Hence, the correct option is (C).