GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen...
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Transcript of GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen...
![Page 1: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/1.jpg)
GAME SHOPA LINEAR PROGRAMMING APPLICATION
![Page 2: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/2.jpg)
THE SETUP
• You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones for the NSA to secretly monitor Apache Junction flash mobs. Your first duty as new owner and store manager is to create an advertising plan based on the budget available. You must figure out how many radio and TV ads to purchase
• Radio ads cost $600 per airing.
• TV ads cost $1200 per airing.
• You total advertising budget is $9,000.
![Page 3: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/3.jpg)
CONSTRAINT 1
• If we let x = radio ads and y = TV ads, write an inequality for our advertising budget.
![Page 4: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/4.jpg)
CONSTRAINT 1
• If we let x = radio ads and y = TV ads, write an inequality for our advertising budget.
• It costs 600 for each radio add, so our radio ad cost is 300x
![Page 5: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/5.jpg)
CONSTRAINT 1
• If we let x = radio ads and y = TV ads, write an inequality for our advertising budget.
• It costs 600 for each radio ad, so our radio ad cost is 300x
• It costs 1200 for each TV ad, so our TV ad cost is 600y
![Page 6: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/6.jpg)
CONSTRAINT 1
• If we let x = radio ads and y = TV ads, write an inequality for our advertising budget.
• It costs 600 for each radio ad, so our radio ad cost is 300x
• It costs 1200 for each TV ad, so our TV ad cost is 600y
• Our total budget is 9000, so our ad costs have to be less than or equal to that.
![Page 7: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/7.jpg)
CONSTRAINT 2
• The television station called to say that we are only allowed to purchase up to 6 TV ads on their Saturday morning gaming retrospective. Write an inequality for this constraint.
![Page 8: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/8.jpg)
CONSTRAINT 2
• The television station called to say that we are only allowed to purchase up to 6 TV ads on their Saturday morning gaming retrospective. Write an inequality for this constraint.
![Page 9: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/9.jpg)
CONSTRAINT 3
• The radio station has informed us that their DJ threatened to quit if he had to listen to more than one add from a game shop per show. They are limiting us to 7 radio ads. Write an inequality for this constraint.
![Page 10: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/10.jpg)
CONSTRAINT 3
• The radio station has informed us that their DJ threatened to quit if he had to listen to more than one add from a game shop per show. They are limiting us to 7 radio ads. Write an inequality for this constraint.
![Page 11: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/11.jpg)
CONSTRAINT 4
• It is impossible to buy a negative number of TV ads. Write an inequality for this constraint.
![Page 12: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/12.jpg)
CONSTRAINT 4
• It is impossible to buy a negative number of TV ads. Write an inequality for this constraint.
![Page 13: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/13.jpg)
CONSTRAINT 5
• It is impossible to buy a negative number of radio ads. Write an inequality for this constraint.
![Page 14: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/14.jpg)
CONSTRAINT 5
• It is impossible to buy a negative number of radio ads. Write an inequality for this constraint.
![Page 15: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/15.jpg)
GRAPHING THE CONSTRAINTS
![Page 16: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/16.jpg)
GRAPHING THE CONSTRAINTS
![Page 17: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/17.jpg)
GRAPHING THE CONSTRAINTS
![Page 18: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/18.jpg)
GRAPHING THE CONSTRAINTS
![Page 19: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/19.jpg)
GRAPHING THE CONSTRAINTS
![Page 20: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/20.jpg)
GRAPHING THE CONSTRAINTS
![Page 21: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/21.jpg)
GRAPHING THE CONSTRAINTS
![Page 22: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/22.jpg)
GRAPHING THE CONSTRAINTS
![Page 23: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/23.jpg)
GRAPHING THE CONSTRAINTS
![Page 24: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/24.jpg)
GRAPHING THE CONSTRAINTS
Points of Intersection(0,0)(0,6)(7,0)
![Page 25: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/25.jpg)
GRAPHING THE CONSTRAINTS
Points of Intersection(0,0)(0,6)(7,0)(7,4)(3,6)
![Page 26: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/26.jpg)
RADIO ADS
Number of radio ads
Increase in game
sales
0 05 7252 2506 9004 4503 4005 7503 6002 3504 5753 4505 7001 150
2 3256 950
![Page 27: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/27.jpg)
RADIO ADS
Number of radio ads
Increase in game
sales
0 05 7252 2506 9004 4503 4005 7503 6002 3504 5753 4505 7001 150
2 3256 950
![Page 28: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/28.jpg)
RADIO ADS
Number of radio ads
Increase in game
sales
0 05 7252 2506 9004 4503 4005 7503 6002 3504 5753 4505 7001 150
2 3256 950
![Page 29: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/29.jpg)
RADIO ADS
Number of radio ads
Increase in game
sales
0 05 7252 2506 9004 4503 4005 7503 6002 3504 5753 4505 7001 150
2 3256 950
y = 150x
![Page 30: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/30.jpg)
TV ADS
Number of TV
ads
Increase in game sales
1 1008 7256 5907 7254 3758 8005 4409 9002 1506 6303 3007 6404 4102 275
5 560
![Page 31: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/31.jpg)
TV ADS
Number of TV
ads
Increase in game sales
1 1008 7256 5907 7254 3758 8005 4409 9002 1506 6303 3007 6404 4102 275
5 560
![Page 32: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/32.jpg)
TV ADS
Number of TV
ads
Increase in game sales
1 1008 7256 5907 7254 3758 8005 4409 9002 1506 6303 3007 6404 4102 275
5 560
![Page 33: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/33.jpg)
TV ADS
Number of TV
ads
Increase in game sales
1 1008 7256 5907 7254 3758 8005 4409 9002 1506 6303 3007 6404 4102 275
5 560
y = 100x
![Page 34: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/34.jpg)
OBJECTIVE FUNCTION
•Write an objective function for game sales. (Hint: Think about how each TV and radio ad affects sales.)
![Page 35: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/35.jpg)
OBJECTIVE FUNCTION
•Write an objective function for game sales. (Hint: Think about how each TV and radio ad affects sales.)
• f(x, y) = 150x + 100y
![Page 36: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/36.jpg)
OBJECTIVE FUNCTION
•Write an objective function for game sales. (Hint: Think about how each TV and radio ad affects sales.)
• f(x, y) = 150x + 100y
• Substitute the coordinates of the vertices into the objective function. Vertex Point Objective Function Total Sales
(0, 0)
(7, 0)
(0, 6)
(7, 4)
(3, 6)
![Page 37: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/37.jpg)
OBJECTIVE FUNCTION
•Write an objective function for game sales. (Hint: Think about how each TV and radio ad affects sales.)
• f(x, y) = 150x + 100y
• Substitute the coordinates of the vertices into the objective function. Vertex Point Objective Function Total Sales
(0, 0) 150(0) + 100(0)
(7, 0) 150(7) + 100(0)
(0, 6) 150(0) + 100(6)
(7, 4) 150(7) + 100(4)
(3, 6) 150(3) + 100(6)
![Page 38: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/38.jpg)
OBJECTIVE FUNCTION
•Write an objective function for game sales. (Hint: Think about how each TV and radio ad affects sales.)
• f(x, y) = 150x + 100y
• Substitute the coordinates of the vertices into the objective function. Vertex Point Objective Function Total Sales
(0, 0) 150(0) + 100(0) 0
(7, 0) 150(7) + 100(0) 1050
(0, 6) 150(0) + 100(6) 600
(7, 4) 150(7) + 100(4) 1450
(3, 6) 150(3) + 100(6) 1050
![Page 39: GAME SHOP A LINEAR PROGRAMMING APPLICATION. THE SETUP You are the new owner of a game shop in Queen Creek. The previous owner is now programming drones.](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e705503460f94b6d416/html5/thumbnails/39.jpg)
OBJECTIVE FUNCTION
•Write an objective function for game sales. (Hint: Think about how each TV and radio ad affects sales.)
• f(x, y) = 150x + 100y
• Substitute the coordinates of the vertices into the objective function. Vertex Point Objective Function Total Sales
(0, 0) 150(0) + 100(0) 0
(7, 0) 150(7) + 100(0) 1050
(0, 6) 150(0) + 100(6) 600
(7, 4) 150(7) + 100(4) 1450
(3, 6) 150(3) + 100(6) 1050