Question

The corner points of the feasible region determined by the following system of linear inequalities:
`2x+yge10, x+3yle15,x,yge0` are `(0,0),(5,0),(3,4)` and `(0,5)`. Let `Z=px+qy`, where `p,qge0`. Condition on `p` and `q` so that the maximum of `Z` occurs at both `(3,4)` and `(0,5)` is:
(a) `p=q` (b) `p=2q` (c) `p=eq` (d) `q=3p`

Answer 1

(d) Maximum value of `Z` is unique. Given that the maximum value of `Z` is obtained at two points `(3,4)` and `(0,5)`.
`:.` Value of `Z` at `(3,4)=` value of `Z` at `(0,5)`
`impliesp(3)+q(4)=p(0)+q(5)`
`implies3p+4q=5qimplies3p=q`