The maximum value of $z=50 x+15 y$ subject to the constraints $x+y \leq 60 ; 5 x+y \leq 100 ; x \geq 0 ; y \geq 0$ is at the point

• A

  $2650,(50,10)$
• B

  $1000,(20,0)$
• C

  $900,(0,60)$
• Correct answer
  D

  $1250,(10,50)$

Solution

$\mathrm{Z}_{\text {max. }}$ at $(10,50)$ $\begin{aligned} & Z_{\text {max. }}=50 \times 10+15 \times 50 \\ & =500+750 \\ & =1250\end{aligned}$

Hence, the correct answer is option: 'D'.