A logging company has one saw with which it makes plywood and pressure-treated wood. Each
piece of plywood requires 20 minutes on the saw and uses 6 eight-foot logs. Each piece of
pressure-treated wood requires 20 minutes on the saw and uses 1 eight-foot log. The saw is
available 10 hours a day, and the logging company can obtain 200 eight-foot logs a day. The
plywood sells for $50 each, and the pressure-treated wood sells for $10 each. Find the maximum
solution.
Plywood = 30, Pressure treated wood = 0, unused labor = 0, unused material = 20, profit = 50
A company makes two products, televisions and DVD players. The televisions require two hours
of labor and $100 of materials per television. The profit per television is $300. The DVD player
requires three hours of labor and $50 of materials per DVD player. The profit per player is
$150. The company can afford to spend $1000 each week for the cost of the material. If an
employee works forty hours a week, how many televisions and/or DVD players should the
employee make in order to maximize the company’s profit?
Televisions = 10, DVD players = 0, unused labor = 20, unused material= 0, profit = 3,000
OR TVs = 5 and DVD = 10 also makes a profit of $3,000
You are given a test where computation problems are worth 6 points and word problems are worth 10
points. It takes you 2 minutes to solve a computation problem and 4 minutes to solve a word
problem. You have 40 minutes to take the test and can answer no more than 12 problems. How
many of each problem should you answer to get the most points?
Let x = number of computation problems
Let y = number of word problems
x 0, y 0

Constraints: 2x 4 y 40

x  y 12
Total Points = 6x+10y
Corner Points are: (0, 0) (0, 10) (4, 8) (12, 0)
The maximum number of points would be 104 if you answer 4 computation problems and 8
wordproblems.
A manufacturer of skis produces two types; downhill and cross-county. Use the following table
to determine how many of each kind of ski should be produced to achieve a maximum profit. What is
the maximum profit?
Let x = # of Downhill Skis
Let y = # of Cross Country Skis
x  0, y 0

2x 1 y 40
Constraints: 
1x 1 y 32
Profit = 70x 50 y

Corner Points are: (0, 0) (0, 32)
(8,24) (20, 0)
Downhill Cross- Max
Country time
available
Manufacturing 2 hours 1 hour 40
time per ski
hours
Finishing time 1 hour
1 hour 32
per ski
hours
Profit per ski $70
$50
The maximum profit of $1760 would be made with 8 Downhill Skis and 24 Cross Country Skis.

Food and clothing are shipped to survivors of a natural disaster. Each carton of food will feed
12 people, while each carton of clothing will help 5 people. Each 20-cubic-foot box of food
weighs 50 pounds and each 10-cubic-foot box of clothing weighs 20 pounds. The commercial
carriers transporting food and clothing are bound by the following constraints:
The total weight cannot exceed 19,000 pounds.
The total volume must be no more than 8000 cubic feet.
How many cartons of food and clothing should be sent with each plane shipment to maximize
the number of people who can be helped?
x = Number of cartons of FOOD
y = Number of cartons of CLOTHING
Constraints:
50x 20 y 19000

20x 10 y 8000
Objective Function:
Help 12x 5y
Vertices:
(0, 800)
(300, 200)
(380, 0)
-->
-->
-->
12(0) + 5(800) = 4000 people
12(300) + 5(200) = 4600 people
12(380) + 5(0) = 4560 people
Answer:
Send 300 cartons of food and 200 cartons of clothing to
help 4600 people.
This region
should be
shaded - it
is the
feasible
region.