• # question_answer The minimum value of the objective function $z=2x+10y$ for linear constraints $x\ge 0,\ y\ge 0$, $x-y\ge 0$, $x-5y\le -5$, is A)                 10           B)                 15 C)                 12           D)                 8

Required region is unbounded whose vertex is $\left( \frac{5}{4},\frac{5}{4} \right)$. Hence the minimum value of objective function is $=2\times \frac{5}{4}+10\times \frac{5}{4}=15$.