Linear Programming
Ex1) Use the system of constraints below to maximize the
objective function z = -0.4x + 3.2y.
x  0

y  0
x  5

x  y  7
x  2y  4

y  x  5
Corner Points
Linear Programming
Ex1) Use the system of constraints below to maximize the
objective function z = -0.4x + 3.2y.
(x,y)
(0,2)
(0,5)
(1,6)
(4,0)
(5,0)
(5,2)
z = -0.4x + 3.2y
Linear Programming
Ex2) Use the system of constraints below to minimize the
objective function z = 2x + 3y.
x  0

y 0


x  6

y  5

x  y  2
Corner Points
Linear Programming
Ex2) Use the system of constraints below to minimize the
objective function z = 2x + 3y.
(x,y)
(0,2)
(0,5)
(2,0)
(6,0)
(6,5)
z = 2x + 3y
Linear Programming
Ex3) A calculator company makes scientific and graphing
calculators. There is a demand for at least 100 scientific and
80 graphing calculators a day; however, due to materials, no
more than 200 scientific and 170 graphing calculators can be
made daily. To satisfy a shipping contract, at least 200 calculators must
be shipped each day. If each scientific calculators results in a loss of $2,
but each graphing calculator gains a profit of $5, how many of each
type should be made to maximize profit?
a) Identify the system of constraints
and the objective function.
x = sci calcs
y = graph calcs





Linear Programming
b) Graph the system of constraints to find the corner points
x 100

y  80


x  200

y

170


x  y  200
Corner Points
Linear Programming
c) Plug in the corner points to determine what amount of
each type of calculator would maximize profit.
(x,y)
(100,100)
(100,170)
(120,80)
(200,80)
(200,170)
P = -2x + 5y
Linear Programming
Ex4) A toy manufacturer makes bikes and wagons. It requires
2 hours of machine time and 4 hours of painting time to
produce a bike. It requires 3 hours of machine time and 2
hours of painting time to produce a wagon. There are 12
hours of machine time and 16 hours of painting time available per day.
The profit on bikes is $12 and the profit on wagons is $10. How many
bikes and wagons should be produced per day to maximize profit?
What is the maximum profit per day?