Question

Maximum value of $12x+3y$ subject to constraints $x\ge 0$, $y\ge 0,x+y\le 5$ and $3x+y\le 9$ is

• A. 15
• B. 36
• C. 60
• D. 40

Answer 1

Answer: (B)

Given, constraints are $x\ge 0,y\ge 0,x+y\le 5$
and $3x+y\le 9$ and $z=12x+3y$

Here, feasible region of $OABC$
At point $O(0,0),z=12(0)+3(0)=0$
At point $A(3,0),z=12(3)+3(0)=36$
At point $B(2,3),z=12(2)+3(3)=33$
At point $C(0,5),z=12(0)+3(5)=15$
Hence, maximum value is 36.