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

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Row 1, Col 1 Solve the system: (-2,-8,-1)

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1,2 Find the minimum and maximum of C=2x+3y subject to: Min of 0 at (0,0) and max of 27 at (0,9)

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1,3 f(n,p)=100n+350p+500 (n=number non-peak hrs, p=number peak hrs) It costs $100 to air a commercial during off-peak hours on the radio and $350 during peak hours. A company charges $500 to make the commercial. 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.

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1,4 Write x-5y-z=14 as a function of x and y. f(x,y)=x-5y-14

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2,1 Solve the system: No solution

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2,2 25 tourist seats Fly-High Airlines sells business class and tourist class seats for its charter flights. To charter a 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?

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2,3 Plane 550 mph, wind 50 mph An 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.

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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

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3,1 Write the equation of the parabola through (-1,-17), (0,-14), and (2,10). y=3x^2+6x-14

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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?

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3,3 DAILY DOUBLE! A pharmacist needs 8 oz of a 50% saline solution. How many ounces of 60% saline solution and 20% saline solution must he use? 6 oz of 60% and 2 oz of 20%

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3,4 NON-MATH QUESTION! What was the original name for Mario in the 1981 arcade game Donkey Kong? Jumpman

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4,1 Describe the solutions to the system in terms of x: Points of the form (x,3-x,6x-11)

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4,2 Trivia Who is known as the Father of Linear Programming? George Dantzig

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4,3 At store A, cameras are available for 15% off. At store B, there is a $300 coupon for all cameras. Assume the lowest priced camera is $700. When does Store A have a better deal? If the price is over $2000

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4,4 (0,0,0) is always a solution If a linear system has the form ax+by+cz=0 dx+ey+fz=0 gx+hy+kz=0 it is called homogeneous. Explain why any homogeneous system has at least one solution.

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8.6 Linear Programming. Linear Program: a mathematical model representing restrictions on resources using linear inequalities combined with a function.

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