100 200 400 300 400 3 Variable Systems Linear Prog. Mixed Applicati ons Leftovers 300 200 400 200 100.
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100 100
200 200
400 400
300
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3 Variable Systems
Linear Prog.
Mixed Applicati
onsLeftovers
300 300 300
200
400
200
100100
Row 1, Col 1
Solve the system:
(-2,-8,-1)
1,2
Find the minimum and maximumof C=2x+3y subject to:
Min of 0 at (0,0) and max of 27 at (0,9)
1,3
f(n,p)=100n+350p+500 (n=number non-peak hrs, p=number peak hrs)
It costs $100 to air a commercialduring off-peak hours on the radio and$350 during peak hours. A company
charges $500 to make thecommercial. Write a model for
the total amount that will be spent making and airing the commercial as a function of
the number of times it is aired during off-peak and peak hours.
1,4
Write x-5y-z=14as a function of x and y.
f(x,y)=x-5y-14
2,1
Solve the system:
No solution
2,2
25 tourist seats
Fly-High Airlines sells business class and tourist class seats for its charter flights. To
chartera plane at least 5 business class tickets must be sold and at least 9 tourist class tickets must be
sold. The plane does not hold more than 30 passengers. Fly-High makes $40 profit for each
business class ticket sold and $45 profit for each tourist class ticket sold. In order for Fly-
High Airlines to maximize its profits, how many tourist class seats should they sell?
2,3
Plane 550 mph, wind 50 mphAn airplane flying into a head
wind travels the 1800-mile flying distance between two cities in 3 hours and 36 minutes. On the
return flight (with a tail wind), the same distance is traveled in 3
hours. Find the ground speed of the plane and the speed of the wind,
assuming that both remain constant.
2,4
A plane has x-intercept of 4,y-intercept of -5, and z-intercept
of -3. If you were to write the equation of this plane
in standard form, what would be the value of d?
The LCM of 4,-5,-3, which is 60
3,1
Write the equation ofthe parabola through (-1,-17),
(0,-14), and (2,10).
y=3x^2+6x-14
3,2
Sell 6 small sheds
Bob builds tool sheds. He uses 10 sheets of dry wall and 15 studs for a small shed and 15 sheets of dry wall and 45 studs for a large shed. He has available 60 sheets of
dry wall and 135 studs. If Bob makes $390 profit on a small shed and $520 on a
large shed, how many of each type of building should Bob build to maximize his
profit?
3,3
DAILY DOUBLE!A pharmacist needs 8 oz of a 50%saline solution. How many ouncesof 60% saline solution and 20%
saline solution must he use?
6 oz of 60% and 2 oz of 20%
3,4
NON-MATH QUESTION!What was the original namefor Mario in the 1981 arcade
game “Donkey Kong”?
Jumpman
4,1
Describe the solutions to the systemin terms of x:
Points of the form (x,3-x,6x-11)
4,2
TriviaWho is known as the “Father of
Linear Programming”?
George Dantzig
4,3
At store A, cameras are availablefor 15% off. At store B, there
is a $300 coupon for all cameras.Assume the lowest priced
camera is $700. When does StoreA have a better deal?
If the price is over $2000
4,4
(0,0,0) is always a solution
If a linear system has the formax+by+cz=0dx+ey+fz=0gx+hy+kz=0
it is called homogeneous.
Explain why any homogeneous system has at least one solution.
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