A carpenter makes tables and chairs

MATHEMATICS · Single correct · CBSE · Mathematics · Linear Programming · Linear Programming

Problem

A carpenter makes tables (x)(x) and chairs (y)(y). Each table needs 33 hours of carpentry and 22 hours of painting, while each chair needs 22 hours of carpentry and 11 hour of painting. Weekly limits are 120120 carpentry hours and 6060 painting hours. At most twice as many chairs as tables can be made. Profit is Rs 500 per table and Rs 200 per chair. Which set of statements correctly formulates the linear programming problem to maximise weekly profit? (a) Maximise Z=200x+500yZ = 200x + 500y; 3x+2y≤1203x + 2y \le 120, 2x+y≤602x + y \le 60, y≤2xy \le 2x, x≥0x \ge 0, y≥0y \ge 0 (b) Maximise Z=500x+200yZ = 500x + 200y; 3x+2y≤1203x + 2y \le 120, 2x+y≤602x + y \le 60, y≤2xy \le 2x, x≥0x \ge 0, y≥0y \ge 0 (c) Maximise Z=500x+200yZ = 500x + 200y; 3x+2y≥1203x + 2y \ge 120, 2x+y≤602x + y \le 60, y≤2xy \le 2x, x≥0x \ge 0, y≥0y \ge 0 (d) Maximise Z=500x+200yZ = 500x + 200y; 3x+2y≤1203x + 2y \le 120, 2x+y≤602x + y \le 60, y≥2xy \ge 2x, x≥0x \ge 0, y≥0y \ge 0

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