A Small Lumber Company in the Southeast Produces Two Types

question 14

Essay

A small lumber company in the Southeast produces two types of pine boards used in home construction: 2x4s and 2x6s (dimensions in inches).They are attempting to determine how many of each to produce so as to minimize their costs on a per-minute basis.They have sales commitments to produce four 2x4s and two 2x6s per minute, but they think they shouldn't produce any more than eight 2x6s because of market demand.They are also trying to support the community by employing people.Thus they want to keep at least 12 men employed, but only need 2 men to produce each 2x4 and 1 person to produce each 2x6 per minute.It costs them $.50 to produce 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?

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Definitions:

Free Markets

Economic markets that are largely free from government intervention, where prices are determined by supply and demand.

Man Of System

Refers to an individual who believes in strictly applying their own theoretical systems to society, without accommodating for the variability of human nature.

Society Members

Individuals or entities that make up a community or group with shared customs, laws, or institutions.

Chess-Board

A square board used in the game of chess, consisting of 64 squares arranged in an 8x8 grid, alternating in color.