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 o ID: 1033062
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1. Game shopA linear programming Application
2. The setupYou 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 purchaseRadio ads cost $600 per airing. TV ads cost $1200 per airing. You total advertising budget is $9,000.
3. Constraint 1If we let x = radio ads and y = TV ads, write an inequality for our advertising budget.
4. Constraint 1If 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
5. Constraint 1If 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 300xIt costs 1200 for each TV ad, so our TV ad cost is 600y
6. Constraint 1If 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 300xIt costs 1200 for each TV ad, so our TV ad cost is 600yOur total budget is 9000, so our ad costs have to be less than or equal to that.
7. Constraint 2The 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.
8. Constraint 2The 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.
9. Constraint 3The 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.
10. Constraint 3The 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.
11. Constraint 4It is impossible to buy a negative number of TV ads. Write an inequality for this constraint.
12. Constraint 4It is impossible to buy a negative number of TV ads. Write an inequality for this constraint.
13. Constraint 5It is impossible to buy a negative number of radio ads. Write an inequality for this constraint.
14. Constraint 5It is impossible to buy a negative number of radio ads. Write an inequality for this constraint.
15. Graphing the Constraints
16. Graphing the Constraints
17. Graphing the Constraints
18. Graphing the Constraints
19. Graphing the Constraints
20. Graphing the Constraints
21. Graphing the Constraints
22. Graphing the Constraints
23. Graphing the Constraints
24. Graphing the ConstraintsPoints of Intersection (0,0) (0,6) (7,0)
25. Graphing the ConstraintsPoints of Intersection (0,0) (0,6) (7,0) (7,4) (3,6)
26. Radio adsNumber of radio adsIncrease in game sales005725225069004450340057503600235045753450570011502 3256950
27. Radio adsNumber of radio adsIncrease in game sales005725225069004450340057503600235045753450570011502 3256950
28. Radio adsNumber of radio adsIncrease in game sales005725225069004450340057503600235045753450570011502 3256950
29. Radio adsNumber of radio adsIncrease in game sales005725225069004450340057503600235045753450570011502 3256950y = 150x
30. TV ADSNumber of TV adsIncrease in game sales 110087256590772543758800544099002150663033007640441022755560
31. TV ADSNumber of TV adsIncrease in game sales 110087256590772543758800544099002150663033007640441022755560
32. TV ADSNumber of TV adsIncrease in game sales 110087256590772543758800544099002150663033007640441022755560
33. TV ADSNumber of TV adsIncrease in game sales 110087256590772543758800544099002150663033007640441022755560 y = 100x
34. OBJECTIVE FUNCTIONWrite an objective function for game sales. (Hint: Think about how each TV and radio ad affects sales.)
35. OBJECTIVE FUNCTIONWrite an objective function for game sales. (Hint: Think about how each TV and radio ad affects sales.)f(x, y) = 150x + 100y
36. OBJECTIVE FUNCTIONWrite 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 PointObjective FunctionTotal Sales(0, 0)(7, 0)(0, 6)(7, 4)(3, 6)
37. OBJECTIVE FUNCTIONWrite 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 PointObjective FunctionTotal 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)
38. OBJECTIVE FUNCTIONWrite 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 PointObjective FunctionTotal 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
39. OBJECTIVE FUNCTIONWrite 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 PointObjective FunctionTotal 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