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

MATHEMATICS · Multi-part · CBSE · Mathematics · Linear Programming · Linear Programming

Problem

Solve the following optimisation problem in the first quadrant: Constraints : x+y≥4,  2x+y≥6,  x≥0,  y≥0x+y\ge 4,\;2x+y\ge 6,\;x\ge 0,\;y\ge 0. Objective : Minimise Z=7x+5yZ=7x+5y. (a) Sketch the feasible region and list all of its corner points with exact coordinates. (b) Evaluate ZZ at every corner point obtained in part (a) and hence find the minimum value of ZZ together with the point at which it occurs. (c) State, with one supporting reason, whether ZZ possesses a finite maximum value for the same feasible region.

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