If `z=ax+by,a,b,gt0` subject to `xle2,yle2,x+yge3,xge0,yge0` has minimum value at (2,1) only, then . .

Options

A. `agtb`
B. `a=b`
C. `a lt b`
D. `a=1+b`

Answer

C

Explanation

We have, `z=ax+by,a,b gt 0`
Subject to constrants `x le 2, y le 2, x+y ge 3x,y ge 0`
On taking given constraints are equation, we get the following graph

here, ABCA is the required feasible region whose corner ponts are A(2,1), B(1,2) and C(2,2).
Since, it is given that z=ax+by, a,bgt0
has minimum value at (2,1).
`therefore`Value of z at (2,1)ltvalue of z at (1,2)
`implies2a+b lt a +2b`
`implies a lt b`