Question

Refer to question 12. What will be the minimum cost?

Answer 1

Referring to solution 12, we have minimise Z=400x +200y, subject to $5x+2y\ge 30$,
$2x+y\le 15,x\le y,x\ge 0,y\ge 0$.
On solving x -y =0 and 5x+2y =30, we get
$y=\frac{30}{7},x=\frac{30}{7}$

On solving x -y =0 and 2x +y =15, we get x =5, y =5
So, from the shaded feasible region it is clear that coordinates of corner points are (0,15), (5,5) and $(\frac{30}{7},\frac{30}{7})$

$\begin{array}{cc}\text{Corner points}& \text{Corresponding value of Z=400x+200y}\\ (0,15)& 3000\\ (5,5)& 3000\\ (\frac{30}{7},\frac{30}{7})& 400\times \frac{30}{7}+200\times \frac{30}{7}=\frac{18000}{7}\\ & =257143\leftarrow Minimum\end{array}$
Hence, the minimum cost is Rs 2571.43