Question

The maximum value of $2x+y$ subject to $3x+5y\le 26$ and $5x+3y\le 30,x\ge 0,y\ge 0$

• A. $12$
• B. $11.5$
• C. $10$
• D. $17.33$

Answer 1

Answer: (B)

$11.5$

Given inequalities are $3x+5y\le 26$ and $5x+3y\le 30$

both $x,y\ge 0$,

Adding the two inequalities gives $x+y\le 7$,

$⟹3x+3y\le 21$

$⟹y\le \frac{5}{2},x\le \frac{9}{2}$,

All the inequalities hold,

$\therefore$ the value of $2x+y$ is $9+2.5=11.5$.