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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

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  1. that1chick
    • 2 years ago
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    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
    • 2 years ago
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    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
    • 2 years ago
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    So what do you get when you translate "Produce at least 20 of product #2"

  4. that1chick
    • 2 years ago
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    y>= 20?

  5. jim_thompson5910
    • 2 years ago
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    you got it

  6. jim_thompson5910
    • 2 years ago
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    Therefore, your system should be x >= 30 y >= 20 3x+5y <= 340

  7. that1chick
    • 2 years ago
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    dude, thank you so much! :D

  8. jim_thompson5910
    • 2 years ago
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    yw, the only thing left to do is graph do you know how to do that?

  9. that1chick
    • 2 years ago
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    not with inuqualitites.. help?

  10. jim_thompson5910
    • 2 years ago
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    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
    • 2 years ago
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    To graph y >= 20, you * graph the horizontal line y = 20 * make it a solid line * shade above the solid line

  12. jim_thompson5910
    • 2 years ago
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    to graph 3x+5y <= 340, you * graph the line 3x+5y = 340 * make it a solid line * shade below the line

  13. jim_thompson5910
    • 2 years ago
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    all 3 regions overlap to form the final shaded region

  14. that1chick
    • 2 years ago
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    how would I do 3x+5y <= 340?

  15. jim_thompson5910
    • 2 years ago
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    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
    • 2 years ago
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    Youre amazing! xD

  17. jim_thompson5910
    • 2 years ago
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    thx, now you just need one more point to graph 3x+5y = 340

  18. that1chick
    • 2 years ago
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    x=30, right?

  19. that1chick
    • 2 years ago
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    hold on, it didn't post part of the directions..

  20. jim_thompson5910
    • 2 years ago
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    alright

  21. that1chick
    • 2 years ago
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    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
    • 2 years ago
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    same problem or different one entirely?

  23. that1chick
    • 2 years ago
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    Same

  24. that1chick
    • 2 years ago
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    I think.. It was just the directions continued

  25. jim_thompson5910
    • 2 years ago
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    alright thx

  26. jim_thompson5910
    • 2 years ago
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    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
    • 2 years ago
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    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
    • 2 years ago
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    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
    • 2 years ago
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    here is the xy axis |dw:1358723166719:dw|

  30. jim_thompson5910
    • 2 years ago
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    now here I'm going to add on the graphs of x = 30, y = 20, and |dw:1358723212768:dw|

  31. jim_thompson5910
    • 2 years ago
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    the shaded region is here |dw:1358723376880:dw| and it includes the surrounding (triangular) boundary

  32. that1chick
    • 2 years ago
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    x would be (30,0) and y would be (0,20) right?

  33. jim_thompson5910
    • 2 years ago
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    what do you mean

  34. that1chick
    • 2 years ago
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    for x>=30 I would graph (0,30) ?

  35. that1chick
    • 2 years ago
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    i mean (30,0)

  36. jim_thompson5910
    • 2 years ago
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    yes you would use any points with an x coordinate of 30

  37. that1chick
    • 2 years ago
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    ok cool

  38. jim_thompson5910
    • 2 years ago
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    were you able to find the points of intersection?

  39. that1chick
    • 2 years ago
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    still working on it

  40. jim_thompson5910
    • 2 years ago
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    alright

  41. that1chick
    • 2 years ago
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  42. that1chick
    • 2 years ago
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    I have the points so far

  43. jim_thompson5910
    • 2 years ago
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    this is what I got (see attached)

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  44. that1chick
    • 2 years ago
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    So I connect them and shade the middle right?

  45. jim_thompson5910
    • 2 years ago
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    those points you got look like they need more points to be able to draw the 3 lines

  46. jim_thompson5910
    • 2 years ago
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    take a look at what I posted and see if that makes sense or not

  47. that1chick
    • 2 years ago
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    It wont open

  48. jim_thompson5910
    • 2 years ago
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    odd, it should work with geogebra your file worked

  49. jim_thompson5910
    • 2 years ago
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    here is a screenshot of the graph

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  50. that1chick
    • 2 years ago
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    So I need to (30,0) and (30,4)

  51. that1chick
    • 2 years ago
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    more points

  52. jim_thompson5910
    • 2 years ago
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    yes 2 points per line

  53. that1chick
    • 2 years ago
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    k I have

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  54. that1chick
    • 2 years ago
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    the screen shot worked (:

  55. jim_thompson5910
    • 2 years ago
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    ok great, the upper horizontal line should be diagonal like in the pic i posted

  56. that1chick
    • 2 years ago
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    so how do I fix that?

  57. jim_thompson5910
    • 2 years ago
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    make it go through the points (0,68) and (30,50)

  58. that1chick
    • 2 years ago
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    Ive never used GeoGebra before

  59. that1chick
    • 2 years ago
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    k

  60. jim_thompson5910
    • 2 years ago
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    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
    • 2 years ago
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    K I got

    1 Attachment
  62. jim_thompson5910
    • 2 years ago
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    ok you got all 3 lines nailed down correctly

  63. jim_thompson5910
    • 2 years ago
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    the shaded region will be the triangle in the middle and it will include the boundary

  64. that1chick
    • 2 years ago
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    Ok awesome! ..how do I shade it?

  65. jim_thompson5910
    • 2 years ago
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    like shown in the attachment

    1 Attachment
  66. jim_thompson5910
    • 2 years ago
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    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
    • 2 years ago
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    Thank you so much!

  68. jim_thompson5910
    • 2 years ago
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    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
    • 2 years ago
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    So the shaded region would be P = 10x + 15y, right?

  70. jim_thompson5910
    • 2 years ago
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    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
    • 2 years ago
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    no it won't, the shaded region is done

  72. jim_thompson5910
    • 2 years ago
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    what are the points of intersection

  73. that1chick
    • 2 years ago
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    Oh! I plug in the x and y coordinates into P = 10x + 15y

  74. jim_thompson5910
    • 2 years ago
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    yep, you find the x,y coordinates of these three intersections

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  75. jim_thompson5910
    • 2 years ago
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    then you plug them into P = 10x + 15y

  76. that1chick
    • 2 years ago
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    Okays thank you (:

  77. jim_thompson5910
    • 2 years ago
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    the ordered pair that gives you the largest value of P is the winner

  78. that1chick
    • 2 years ago
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    cool

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