Question

A small construction firm specializes in building and selling single-family homes. The firm offers two basic types of houses, model A and model B. Model A houses require 4,000 labor hours, 2 tons of stone, and 2,000 board feet of lumber. Model B houses require 10,000 labor hours, 3 tons of stone, and 2,000 board feet of lumber. Due to long lead times for ordering supplies and the scarcity of skilled and semiskilled workers in the area, the firm will be forced to rely on its present resources for the upcoming building season. It has 400,000 hours of labor, 150 tons of stone, and 200,000 board feet of lumber. What mix of model A and B houses should the firm construct if model A yields a profit of $4,000 per unit and model B yields $7,000 per unit? Assume that the firm will be able to sell all the units it builds.

Answer 1

Decision variables:

Let A = No of Model A to construct

B = No of model B to construct

Objective function is to maximize the profit

Z = max 4000A + 7000B

Constraints:

4000A + 10000B <= 400000 (Labor hours available)

2A + 3B <= 150 (Stones available)

2000A + 2000B <= 200000

A,B >=0

Solving using Excel solver

A = 37.5

B = 25

Profit Z = 325000