question_answer

The co-ordinates of the point for minimum value of \[z=7x-8y\]subject to the conditions\[x+y-20\le 0\], \[y\ge 5,\,\] \[x\ge 0\], \[y\ge 0\] is [DCE 2005]

A)                 (20, 0)  

B)                 (15, 5)

C)                 (0, 5)     

D)                 (0, 20)

Correct Answer: D

Solution :

                Obviously,\[z=7x-8y\] will be minimum at (0, 20)                                 \ Min z = 7 × 0 ? 8 × 20 = ?160.