Linear Programming
Notes # ____
EQ: How do I find the maximum or minimum value of an expression using linear programming?
Example 1: A coffee shop sells two types of drinks: espressos and cappuccinos. The profit on
an espresso is $1. The profit on a cappuccino is $2.50. Today, the shop has enough beans to
make 200 drinks. The shop only has enough cups to sell 125 cappuccinos. The manager wants
to know the maximum profit the coffee shop can earn today.
a.) Name your variables and write down the quantities they represent.
b.) Write an equation to model the amount of profit the shop will earn.
c.) Write a system of inequalities that models the constraints on how many espressos and
cappuccinos the shop can make.
Below – fill in some possible combinations for how much profit the store can earn.
# Espressos
# Cappuccinos
Total coffee drinks
Profit earned
d.) What is the maximum profit the shop can earn today?
Example 2: Jim’s furniture shop produces bookcases and tables. Bookcases each yield a profit
of $50. Tables each yield a profit of $40. Each bookcase takes 8 hours to make. Each table
takes 5 hours. Jim works 40 hours a week. Every week, he must make at least one table and at
least one bookcase. He wants to know the most profitable way to balance his time between
making tables and bookcases.
a.) Name your variables and write down the quantities they represent.
b.) Write an equation to model the amount of profit Jim can earn.
c.) Write a system of inequalities that models the constraints on how many bookcases and
tables Jim can make.
# Bookcases
# Tables
Time spent
Profit earned
d.) What is the maximum profit Jim can earn in a week?
You Do: Clara makes and sells clothing. The fabric she uses comes in 10-yard bolts. A dress
uses 4 yards of fabric. A skirt uses 2.5 yards. A dress nets $30 profit; a skirt nets $20 profit.
Clara wants to know the maximum profit she can earn from one bolt of fabric.
a.) Name your variables and write down the quantities they represent.
b.) Write an equation to model the amount of profit Clara can earn.
c.) Write a system of inequalities that models the constraints on how many dresses and
skirts Clara can make
# Dresses
# Skirts
Yards of fabric used
d.) What is the maximum profit Jim can earn in a week?
Profit earned
Linear Programming
Notes # ____
EQ: How do I find the maximum or minimum value of an expression using linear programming?
You Do: As a receptionist for a veterinarian, one of Antonio’s tasks is to schedule
appointments. He allots 20 minutes for a routine office visit and 40 minutes for a surgery. The
veterinarian cannot do more than 6 surgeries each day. The office has 7 hours available for
appointments. A routine office visit earns $55 profit for the office, and most surgeries earn $125
profit.
a)
b)
c)
d)