Mathematics

Problem

Solve the following optimisation problem in the first quadrant: Constraints :

x+y\ge 4,\;2x+y\ge 6,\;x\ge 0,\;y\ge 0

. Objective : Minimise

Z=7x+5y

. a. (a) Sketch the feasible region and list all of its corner points with exact coordinates. b. (b) Evaluate

Z

at every corner point obtained in part (a) and hence find the minimum value of

Z

together with the point at which it occurs. c. (c) State, with one supporting reason, whether

Z

possesses a finite maximum value for the same feasible region.