Question

The minimum value of $z=10x+25y$ subject to $0\le x\le 3,0\le y\le 3,x+y\ge 5$ is?

• A. $80$
• B. $95$
• C. $105$
• D. $30$

Answer 1

Answer: (A)

$80$

From graph it is evident that (x,y) satisfying all required conditions for which z is minimum must lie on x+y=5,

So, for finding minimum we can rewrite z as $z=10(5-y)+25y=15y+50$

Lower the value of y, lower is value of z . The minimum value of y which satisfy all required condition is 2 which is also evident from graph.

So, minimum value of z is $15\left(2\right)+50=80$