Notes: Linear Programming: Linear Programming is a method of finding a maximum or minimum value of a
function that satisfies a given set of conditions called constraints. The solution to the set of constraints can be
graphed as a feasible region. A constraint is one of the inequalities in a linear programming problem.
1. Jessica needs to earn at least $360 a week for a ski vacation she is planning with her friends. She can work a
total of no more than 25 hours a week at her two jobs. She builds web pages for $18 an hour and babysits for $9
an hour. Write and graph a system of linear inequalities that shows the number of hours she can work at each job
during the week so that she can earn the money needed for the ski vacation.
2. Fund-raising: A charity is selling T-shirts in order to raise money. The cost of a T-shirt is $15 for adults and
$10 for students. The charity needs to raise at least $3,000 and has only 250 T-shirts. Write and graph a system
of inequalities that can be used to determine the number of adult and student T-shirts the charity must sell.
3. A small community is trying to establish a public transportation system made up of large and small buses. The
community can spend no more than $180,000 for the system and no more than $1,200 per month for maintenance.
The community can purchase a small bus for $10,000 and maintain it for $75 per month. The large buses cost
$20,000 each and can be maintained for $100 per month. Each large bus carries a maximum of 15 passengers, and
each small bus carries a maximum of 7 passengers. Find the maximum number of passengers that can be
transported during one month for the given constraints.
4. Dentistry: Dr. Lee's dentist practice is open for 7 hours each day. His receptionist schedules appointments,
allowing a half hour for a cleaning and one hour to fill a cavity. He charges $40 for a cleaning and $95 for a
filling. Dr. Lee cannot do more than 4 fillings per day. Find the number of each type of appointment that
maximizes Dr. Lee's income for the day.
5. Office Space: You need to buy some filing cabinets. You know that Cabinet X costs $10 per unit, requires six
square feet of floor space, and holds eight cubic feet of files. Cabinet Y costs $20 per unit, requires eight
square feet of floor space, and holds twelve cubic feet of files. You have been given $140 for this purchase,
though you don't have to spend that much. The office has room for no more than 72 square feet of cabinets.
How many of which model should you buy, in order to maximize storage volume?