Linear Programming Practice Name________________________________
1. A company manufactures 2 different cell phone cases, Angry Birds and Star Wars, using 2 different machines, A and B. The table shows how many minutes are required on each machine per day in order to produce the cell phone cases.
Machine Angry Birds Star Wars Min. Available
A 4 min 6 min 24
B 2 min 1 min 8
The company makes a $3 profit on each Angry Birds case and a $5 profit on each
Star Wars case that it sells.
Let x = # of Angry Birds cases and y = # of Star Wars cases.
(a) Write an objective function to maximize the profit.
(b) Write the constraints,
graph the inequalities
and shade the feasible
region.
(c) Name all the vertices and find the value of the objective function for each vertex.
Vertex Value of the objective function
(d) What is the maximum profit the company can make?
(e) How many of each case should they produce to make the maximum profit?

2. Annie wants to plant alfalfa and corn. Each crop requires 1 hour per ton to plant and there are 500 hours available for planting. Alfalfa requires 2 hours per ton to harvest, corn requires 3 hours per ton to harvest and there are 1200 hours available for harvesting. She wants to plant at least 150 tons of alfalfa. The profit on 1 ton of alfalfa is $250 and the profit on 1 ton of corn is $350.
Process Alfalfa Corn Hours
Available
Planting hrs. hrs. hrs.
Harvesting hrs. hrs. hrs.
Let x = # tons of alfalfa and y = # tons of corn
(a) Write an objective function to maximize the profit.
(b) Write the constraints,
graph the inequalities
and shade the feasible
region.
(
You should have a total of 4 constraints)
(c) Name all the vertices and find the value of the objective function for each vertex.
Vertex Value of the objective function
(d) What is the maximum profit Annie can earn?
(e) How many tons of each crop should she plant to make the maximum profit?

3. A company manufactures 2 different models of bicycles. The time (in hours) required for
Assembling,
Painting and Packaging each model is shown below. The total time available for Assembling is
600 hrs., for Painting is 280 hrs. and for Packaging is 480 hrs.
Process
Assembling
Painting
Hours
Model A
2 hours
2 hours
Hours
Model B
3 hours
1 hour
Packaging 4 hour 1 hour
The company makes a $45 profit for Model A and a $50 profit for Model B that is sells.
Let x = # of Model A bicycles and y = # of Model B bicycles.
(a) Write an objective function to maximize the profit.
(b) Write the constraints,
graph the inequalities
and shade the feasible
region.
(c) label the x and y axis with what they are representing.
(d) Name an ordered pair that satisfies the constraints.
(e) Explain what the ordered pair represents in the context of the situation.

4. A company manufactures 2 different video games, Mathman and Superbrain, using 3 different machines, A, B, and C. The table shows how many hours are required on each machine per day in order to produce a game.
Machine Mathman
A 1 hour
B
C
1 hour
3 hours
Superbrain Hours Available
3 hours
1 hour
1 hour
18
8
18
The company makes a $60 profit on each Mathman and a $40 profit on each Superbrain that is sells.
Let x = # Mathman video games and y = # Superbrain video games.
(a) Write an objective function to maximize the profit.
(b) Write the constraints,
graph the inequalities
and shade the feasible
region.
(c) Name all the vertices and find the value of the objective function for each vertex.
Vertex Value of the objective function Vertex Value of the objective function
(d) What is the maximum profit the company can make?
(e) How many of each game should they produce to make the maximum profit?