Transcript Linear Programming

Linear Programming
Healthy Animals
Algebra Standards
 MM3A6. Students will solve linear
programming problems in two
variables.
 a. Solve systems of inequalities in two
variables, showing the solutions graphically.
 b. Represent and solve realistic problems
using linear programming.
Healthy Animals
What does the term constraint mean?
Read the problem situation for Healthy
Animals on page 46.
How many constraints are there in the
problem?
What are they?
Healthy Animals
Each group needs a sheet of chart paper
1. Choose variables to represent the
amount of each type of food that Curtis
will include in the daily diet. State clearly
what the variables represent
2. Use your variables to write inequalities to
describe the constraints of the situation.
Healthy Animals – Homework 6
Individual assignment – Each person needs
graph paper and three different colored
pencils or markers.
Make a graph of each of your constraints.
Graph each constraint on a separate set of
axes. Be sure to label your axes and show
their scales.
Healthy Animals – Feasible Diets
 As a group, decide on a scale that can be
used to graph all of your inequalities on
the same graph.
 Make one graph that shows all the
constraints. Color or highlight the region of
the graph that satisfies all the constraints.
Curtis Makes Choices
Curtis goes into the pet store to buy a substantial
supply of food for his pet. He sees that Food A
costs $2 per pound and Food B costs $3 per
pound. Since he intends to vary his pet’s diet
from day to day anyway, he isn’t especially
concerned about how much he buys of each
type of food.
Suppose he has $30 to spend. What are some
combinations he can buy?
Suppose he has $50 to spend. What are some
combinations he can buy?
What have we done?
MM3A6. Students will solve linear
programming problems in two
variables.
 a. Solve systems of inequalities in two
variables, showing the solutions graphically.
 b. Represent and solve realistic problems
using linear programming.