Linear Programming

1
Linear Programming

• Healthy Animals

2
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.

3
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?

4
Healthy Animals

• Each group needs a sheet of chart paper
• 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
• Use your variables to write inequalities to
  describe the constraints of the situation.

5
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.

6
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.

7
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 pets
  diet from day to day anyway, he isnt 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?

8
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.