100 200 400 300 400 3 Variable Systems Linear Prog. Mixed Applicati ons Leftovers 300 200 400 200 100.

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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.