Mathematics

Problem

Let

x

and

y

be non-negative real numbers satisfying

x+y\ge 3

. For a real parameter

k

define

W=(k-2)x+(k+1)y

. a. (i) Sketch the feasible region represented by

x+y\ge 3,\;x\ge 0,\;y\ge 0

. b. (ii) Determine all real values of

k

for which

W

attains a finite minimum value over the feasible region. c. (iii) Determine all real values of

k

for which

W

attains a finite maximum value over the feasible region.