Section 3.2

Linear Programming

A function subject to a system of constraints to be optimized (maximized or minimized)

is called an objective function.

A system of equalities or inequalities to which an objective function is subject to are

called constraints.

An objective function subject to a system of constraints is called a linear programming

problem.

Example 1: The Soundex Company produces two models of clock radios. Each model A

requires 15 min of work on assembly line I and 10 min of work on assembly line II. Each

model B requires 10 min of work on assembly line I and 12 min of work on assembly line

II. At most, 23 hr of assembly time on line I and 22 hr of assembly time on line II are

available per Soundex’s work day. It is anticipated that Soundex will realize a profit of

$12 on each model A and $10 on each model B. How many clock radios of each model

should be produced per day in order to maximize Soundex’s profit?

a. Define your variables.

b. Construct and fill in a table.

c. State the Linear Programming Problem. Do not solve. (We’ll do this in the next

section.)

Section 3.2 – Linear Programming 1