Answer to Question #197900 in Operations Research for Tavlene Singh

Question

A furniture company manufactures dining room tables and chairs. The company has 150 hours of assembly time available per week and workers must spend at least 100 hours on finishing per week. A table requires 540 minutes for assembly and 180 minutes for finishing. A chair requires 150 minutes for assembly and 60 minutes for finishing. Each table is sold for R4 000 and each chair for R1 500. If x is the number of tables and y the number of chairs produced per week, the constraints and the objective function of the company are [1] 2,5x + y ≥ 1 500; 9x + 3y ≤ 4 000; x, y ≥ 0; π = 150x + 100y. [2] 9x + 2,5y ≥ 150; 3x + y ≤ 100; x, y ≥ 0; T C = 4 000x + 1 500y. [3] 9x + 2,5y ≤ 150; 3x + y ≥ 100; x, y ≥ 0; T R = 4 000x + 1 500y. [4] 540x + 150y ≥ 150; 180x + 60y ≤ 100; π = 4x + 1,5y.

Answer 1

For assembly time:

$540x+150y\le 150\cdot60\implies 9x+2.5y\le 150$

For finishing time:

$180x+60y\le 100\cdot60\implies 3x+y\le 100$

For profit:

$\pi=4000x+1500y$

Answer: [2] 9x + 2,5y ≥ 150; 3x + y ≤ 100; x, y ≥ 0; T C = 4 000x + 1 500y