## that1chick 2 years ago I'm not asking for you to do my work for me, just help me create a system of inequalities please! • The name of your company • The type of business (i.e., clothing, electronics, furniture, etc.) • Two products your company will make • Assign variables to the two products; please use x and y • A system of inequalities based on the following information o Produce at least 30 of product #1. o Produce at least 20 of product #2. o Product #1 costs \$3 per unit to make. o Product #2 \$5 per unit to make. o The total production cost cannot exceed \$340. • Graph the system of inequalities o

1. that1chick

What I have so far: Beyond the Galaxy We create trippy clothes. Such as (product #1:) shirts (x) and (product #2:) skirts (y). 30x+20y<= \$3x+\$5y<=\$340

2. jim_thompson5910

x is the number of items of product 1 so when you make the requirement that you must "Produce at least 30 of product #1", this means x >= 30 So you can produce x = 30, x = 31, x = 32, ... items of product 1 (but nothing less than 30)

3. jim_thompson5910

So what do you get when you translate "Produce at least 20 of product #2"

4. that1chick

y>= 20?

5. jim_thompson5910

you got it

6. jim_thompson5910

Therefore, your system should be x >= 30 y >= 20 3x+5y <= 340

7. that1chick

dude, thank you so much! :D

8. jim_thompson5910

yw, the only thing left to do is graph do you know how to do that?

9. that1chick

not with inuqualitites.. help?

10. jim_thompson5910

to graph x >= 30, follow these steps Step 1) graph the vertical line x = 30 Step 2) make it a solid line Step 3) shade to the right of this solid line

11. jim_thompson5910

To graph y >= 20, you * graph the horizontal line y = 20 * make it a solid line * shade above the solid line

12. jim_thompson5910

to graph 3x+5y <= 340, you * graph the line 3x+5y = 340 * make it a solid line * shade below the line

13. jim_thompson5910

all 3 regions overlap to form the final shaded region

14. that1chick

how would I do 3x+5y <= 340?

15. jim_thompson5910

plug in x = 0 to get 3x+5y = 340 3*0+5y = 340 5y = 340 y = 340/5 y = 68 So one point on the line 3x+5y=340 is (0,68)

16. that1chick

Youre amazing! xD

17. jim_thompson5910

thx, now you just need one more point to graph 3x+5y = 340

18. that1chick

x=30, right?

19. that1chick

hold on, it didn't post part of the directions..

20. jim_thompson5910

alright

21. that1chick

If Product #1 earns a profit of \$10 per unit and Product #2 earns a profit of \$15 per unit, find the combination of Product #1 and Product #2 that will maximize profit. A commercial that could be used to advertise your two products to the general public. You may include a slogan or jingle.

22. jim_thompson5910

same problem or different one entirely?

23. that1chick

Same

24. that1chick

I think.. It was just the directions continued

25. jim_thompson5910

alright thx

26. jim_thompson5910

Let P = combined profit of products #1 and #2 So "If Product #1 earns a profit of \$10 per unit and Product #2 earns a profit of \$15 per unit", then P = 10x + 15y

27. jim_thompson5910

The ideal situation is that there is an ordered pair (x,y) that is within the shaded region and makes P as large as possible

28. jim_thompson5910

It turns out that this ordered pair is a vertex of the shaded region ie, it is formed by the intersection of two of the lines

29. jim_thompson5910

here is the xy axis |dw:1358723166719:dw|

30. jim_thompson5910

now here I'm going to add on the graphs of x = 30, y = 20, and |dw:1358723212768:dw|

31. jim_thompson5910

the shaded region is here |dw:1358723376880:dw| and it includes the surrounding (triangular) boundary

32. that1chick

x would be (30,0) and y would be (0,20) right?

33. jim_thompson5910

what do you mean

34. that1chick

for x>=30 I would graph (0,30) ?

35. that1chick

i mean (30,0)

36. jim_thompson5910

yes you would use any points with an x coordinate of 30

37. that1chick

ok cool

38. jim_thompson5910

were you able to find the points of intersection?

39. that1chick

still working on it

40. jim_thompson5910

alright

41. that1chick

42. that1chick

I have the points so far

43. jim_thompson5910

this is what I got (see attached)

44. that1chick

So I connect them and shade the middle right?

45. jim_thompson5910

those points you got look like they need more points to be able to draw the 3 lines

46. jim_thompson5910

take a look at what I posted and see if that makes sense or not

47. that1chick

It wont open

48. jim_thompson5910

odd, it should work with geogebra your file worked

49. jim_thompson5910

here is a screenshot of the graph

50. that1chick

So I need to (30,0) and (30,4)

51. that1chick

more points

52. jim_thompson5910

yes 2 points per line

53. that1chick

k I have

54. that1chick

the screen shot worked (:

55. jim_thompson5910

ok great, the upper horizontal line should be diagonal like in the pic i posted

56. that1chick

so how do I fix that?

57. jim_thompson5910

make it go through the points (0,68) and (30,50)

58. that1chick

Ive never used GeoGebra before

59. that1chick

k

60. jim_thompson5910

or you can simply type in 3x+5y = 340 into the input bar and it will graph the line 3x+5y = 340 for you

61. that1chick

K I got

62. jim_thompson5910

ok you got all 3 lines nailed down correctly

63. jim_thompson5910

the shaded region will be the triangle in the middle and it will include the boundary

64. that1chick

Ok awesome! ..how do I shade it?

65. jim_thompson5910

like shown in the attachment

66. jim_thompson5910

you can use geogebra to do the shading, or you can use paint like I just did (I used the paint bucket) to fill in the correct region

67. that1chick

Thank you so much!

68. jim_thompson5910

sure thing, you can then easily use geogebra to find the points of intersection then you need to see which points give you the max profit

69. that1chick

So the shaded region would be P = 10x + 15y, right?

70. jim_thompson5910

no that has nothing to do with the shaded region once you find the vertices, you use P = 10x + 15y to test each one

71. jim_thompson5910

no it won't, the shaded region is done

72. jim_thompson5910

what are the points of intersection

73. that1chick

Oh! I plug in the x and y coordinates into P = 10x + 15y

74. jim_thompson5910

yep, you find the x,y coordinates of these three intersections

75. jim_thompson5910

then you plug them into P = 10x + 15y

76. that1chick

Okays thank you (:

77. jim_thompson5910

the ordered pair that gives you the largest value of P is the winner

78. that1chick

cool