Linear Programming-“setting the stage” Linear programming is a mathematical technique used to find the optimal allocation of resources
in the military, business, telecommunications, and other fields.
It got its start during World War II when it became necessary to move huge quantities of people,
materials, and supplies as efficiently and economically as possible.
or
The goal when solving linear programming problems is to
a function. One common scenario is using linear programming to
maximize
.
Linear programming uses systems of inequalities to find the shaded region. But the toughest part
is usually setting up the
and the
for
a problem. Let's practice this first...
Example 1: Lisa has an online jewelry shop where she sells earrings and necklaces. It takes 2 hour to
make one pair of earrings and 1 hour to make one necklace, and she only has 10 hours each week to
make jewelry. In addition, she only has enough materials to make 15 total jewelry items per week.
She makes a profit of $15 on each pair of earrings and $20 on each necklace.
Question: How many pairs of earrings and necklaces should Lisa make each week in order to
maximize her profit, assuming she sells all her jewelry?
a. What are we trying to maximize? Use x to represent the number of earrings and y to
represent the number of necklaces.
b. What "constraints" are there?