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Game shop. A linear programming Application. The setup. - PowerPoint PPT Presentation
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GAME SHOPA LINEAR PROGRAMMING APPLICATION
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.
CONSTRAINT 1
• If we let x = radio ads and y = TV ads, write an inequality for our advertising budget.
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
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
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.
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.
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.
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.
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.
CONSTRAINT 4
• It is impossible to buy a negative number of TV ads. Write an inequality for this constraint.
CONSTRAINT 4
• It is impossible to buy a negative number of TV ads. Write an inequality for this constraint.
CONSTRAINT 5
• It is impossible to buy a negative number of radio ads. Write an inequality for this constraint.
CONSTRAINT 5
• It is impossible to buy a negative number of radio ads. Write an inequality for this constraint.
GRAPHING THE CONSTRAINTS
GRAPHING THE CONSTRAINTS
GRAPHING THE CONSTRAINTS
GRAPHING THE CONSTRAINTS
GRAPHING THE CONSTRAINTS
GRAPHING THE CONSTRAINTS
GRAPHING THE CONSTRAINTS
GRAPHING THE CONSTRAINTS
GRAPHING THE CONSTRAINTS
GRAPHING THE CONSTRAINTS
Points of Intersection(0,0)(0,6)(7,0)
GRAPHING THE CONSTRAINTS
Points of Intersection(0,0)(0,6)(7,0)(7,4)(3,6)
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
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
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
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
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
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
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
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
OBJECTIVE FUNCTION
•Write an objective function for game sales. (Hint: Think about how each TV and radio ad affects sales.)
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
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)
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)
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
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
