question_answer

The maximum value of \[z=5x+2y\], subject to the constraints \[x+y\le 7,\ x+2y\le 10\], \[x,\ y\ge 0\] is                  [AMU 1999]

A)                 10          

B)                 26

C)                 35          

D)                 70

Correct Answer: C

Solution :

                Change the inequalities into equations and draw the graph of lines, thus we get the required feasible region.                                 The region bounded by the vertices \[A(0,\,5),B(4,\,3)\]and \[C(7,\,0)\].                 The objective function is maximum at \[C(7,0)\]and Max\[z=5\times 7+2\times 0=35\].