A Small Lumber Company Produces Two Types of Pine Boards

Essay

A small lumber company produces two types of pine boards used in home construction: 2x4s and 2x6s (dimensions in inches). It is attempting to determine how many of each to produce so as to minimize its costs on a per-minute basis. It has sales commitments to produce four 2x4s and two 2x6s per minute, but the management thinks they should not produce any more than eight 2x6s because of market demand. The company is also trying to support the community by employing people. Thus, it wants to keep at least 12 men employed, but only needs 2 men to produce each 2x4 and 1 person to produce each 2x6 per minute. It costs the company $.50 to produce a 2x4 and $.80 to produce a 2x6 per minute.
a. What is the objective function for this LP problem?
b. What is the constraint for the employment issue, assuming x₁ corresponds to 2x4s?
c. What is the optimal solution point for this problem?
d. What is the optimal value of the objective function?