Question

Refer to question 13. Solve the linear programming problem and detrmine the maximum profit to the manufacturer.

Answer 1

Referring to solution 13, we have
Maximise Z =100x +170y subject to $3x+2y\le 3600,x+4y\le 1800,x\ge 0,y\ge 0$
From the shaded feasible region it is clear that the coordinates of corner points are (0,0), (1200,0),(1080,180)and (0,450).
On solving x+4y =1800 and 3x+2y =3600, we get x=1080 and y =180

$\begin{array}{cc}\text{Corner points}& \text{Corresponding value of Z=100x+170y}\\ (0,0)& 0\\ (1200,0)& 1200\times 100=120000\\ (1080,180)& 100\times 1080+170\times 180=138600\leftarrow Maximum\\ (0,450)& 0+170\times 450=76500\end{array}$
Hence, the maximum profit to the manufacturer is 138600.