1. GAME SHOP A LINEAR PROGRAMMING APPLICATION

2. 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.

3. CONSTRAINT 1 If we let x = radio ads and y = TV ads, write an inequality for our advertising budget.

4. 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

5. 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

6. 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.

7. 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.

8. 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.

9. 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.

10. 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.

11. CONSTRAINT 4 It is impossible to buy a negative number of TV ads. Write an inequality for this constraint.

12. CONSTRAINT 4 It is impossible to buy a negative number of TV ads. Write an inequality for this constraint.

13. CONSTRAINT 5 It is impossible to buy a negative number of radio ads. Write an inequality for this constraint.

14. CONSTRAINT 5 It is impossible to buy a negative number of radio ads. Write an inequality for this constraint.

15. GRAPHING THE CONSTRAINTS

24. Points of Intersection (0,0) (0,6) (7,0)

25. GRAPHING THE CONSTRAINTS Points of Intersection (0,0) (0,6) (7,0) (7,4) (3,6)

26. RADIO ADS Number of radio ads Increase in game sales 00 5725 2250 6900 4450 3400 5750 3600 2350 4575 3450 5700 1150 2325 6950

27. RADIO ADS Number of radio ads Increase in game sales 00 5725 2250 6900 4450 3400 5750 3600 2350 4575 3450 5700 1150 2325 6950

28. RADIO ADS Number of radio ads Increase in game sales 00 5725 2250 6900 4450 3400 5750 3600 2350 4575 3450 5700 1150 2325 6950

29. RADIO ADS Number of radio ads Increase in game sales 00 5725 2250 6900 4450 3400 5750 3600 2350 4575 3450 5700 1150 2325 6950 y = 150x

30. TV ADS Number of TV ads Increase in game sales 1100 8725 6590 7725 4375 8800 5440 9900 2150 6630 3300 7640 4410 2275 5560

31. TV ADS Number of TV ads Increase in game sales 1100 8725 6590 7725 4375 8800 5440 9900 2150 6630 3300 7640 4410 2275 5560

32. TV ADS Number of TV ads Increase in game sales 1100 8725 6590 7725 4375 8800 5440 9900 2150 6630 3300 7640 4410 2275 5560

33. TV ADS Number of TV ads Increase in game sales 1100 8725 6590 7725 4375 8800 5440 9900 2150 6630 3300 7640 4410 2275 5560 y = 100x

34. OBJECTIVE FUNCTION Write an objective function for game sales. (Hint: Think about how each TV and radio ad affects sales.)

35. 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

36. 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 PointObjective FunctionTotal Sales (0, 0) (7, 0) (0, 6) (7, 4) (3, 6)

37. 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 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 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 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 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 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