3.4 Linear Programming Pre-APname ______
Period ______
1. An appliance dealer wishes to stock a maximum of 100 refrigerators and stoves. A refrigerator weighs 200 pounds anda stove weighs 100 pounds. The dealer is limited to a total weight of 12,000 pounds. If the dealer makes a profit of$35 per refrigerator and $20 per stove, how many of each should be stocked for maximum profit?
What will be the profit?
Let x = ______
Let y = ______
Profit equation: P = ______
What are the constraint inequalities?
Vertices ______min/max ______
______
______solution sentence ______
______
2.A carpenter makes bookcases in two sizes, large and small. It takes 6 hours to make a large bookcase and 2 hours to
make a small one. The profit on a large bookcase is $50 and the profit on a small bookcase is $20. The carpenter can
spend only 24 hours per week making bookcases and must make at least 2 of each size per week. How many of each
size must be made per week in order to provide maximum profit? What will the profit be?
Let x = ______
Let y = ______
Profit equation: P = ______
constraints
Vertices ______min/max ______v ______m/m ______
______v ______m/m ______
Solution Sentence ______
3. Craig Browning bakes cookies for the elementary school cookie sale. His chocolate chip cookies sell for $1 a dozen and
his oatmeal cookies sell for $1.50 a dozen. He will bake up to 20 dozen chocolate chip cookies, and up to 40 dozen
oatmeal cookies, but no more than 50 dozen cookies total. Also, the number of oatmeal cookies will be no more than
three times the number of the chocolate chip cookies. How many of each kind should Craig make in order for the
elementary school to make the most money?
Let x = ______
Let y = ______
Profit equation: P = ______
What are the constraint inequalities?
Vertices ______min/max ______
______
______solution sentence ______
4. The Cutting Edge Salon schedules appointments for haircuts for 30 minutes and highlights for one hour. Each haircut
costs $20 and highlights cost $45. The salon wants to schedule no more than 4 highlights per day and at least 3
haircuts per day. Find the number of appointments that produces the maximum income per stylist in a workday of at
most 8 hours.
Let x = the number of haircuts
Let y = the number of highlights
Profit equation: P = ______
What are the constraint inequalities?
Vertices ______min/max ______
______
______
______
Solution sentence ______
______
5. Graph the constraints and shade the feasible region.
Find the coordinates of the vertices of the feasible region.
Given ,analyze the coordinates of the
vertices of the feasible region to determine the maximum value.
Vertices ______min/max ______
______
______
______
Solution sentence ______
______
6. The Stuff-Your-Own Teddy Bear Company sells teddy bears and puppies. To stay in business, it must produce at
least 50 teddy bears each month, but it does not have the facilities to produce more than 130 teddy bears each
month. It also does not have the facilities to produce more than 80 puppies each month. The total production of
teddy bears and puppies cannot exceed 140. The profit on a teddy bear is $15 and the profit per puppy is $12.
To make the maximum profit, how many of each should be made in a month?
Let x = the number of TEDDY BEARS made in one month
Let y = the number of PUPPIES made in one month
Profit equation: P = ______
What are the constraint inequalities?
Vertices ______min/max ______
______
______
______solution sentence ______