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  • one year ago
  • one year ago

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  1. phi Group Title
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    I just noticed the last line: If you must order at least one of each type of table, because without that line I was not getting any of your choices. Can you try to sketch the relations? Let x be the number of type A and y be the number of type B You can order no more than 190 tables this month. that means the sum of x and y must be less than or equal to 190 x+y≤ 190 put this into slope-intercept form: y ≤ -x + 190 plot the line y= -x + 190 shade the area under this line (this is where y is less than the line) can you do that?

    • one year ago
  2. Falkqwer Group Title
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    I'll try :) one sec

    • one year ago
  3. phi Group Title
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    It only shows a bit of the graph. By hand: |dw:1358269570252:dw|

    • one year ago
  4. Falkqwer Group Title
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    OK so what does this tell me now? sorry I'm dumb :(

    • one year ago
  5. phi Group Title
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    We don't go below x=0 (we can't order less than 0) same for y that triangle represents all (x,y) pairs of orders where x+y ≤ 190 (and x+y≥0 we can't order less than 0) if you go outside the triangle you will order too many or a negative number. Neither is allowed.

    • one year ago
  6. phi Group Title
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    you need to make at least $4,610 profit on them It would be good if you could write down the relation (mathematical expression) for this. Hero posted it, but you should try. The profit will be the number of type A's times the profit per type A plus # of B's times profit of a B this sum must be ≥ 4610 Can you write down the expression?

    • one year ago
  7. Falkqwer Group Title
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    29a + 19b >_ 4610

    • one year ago
  8. phi Group Title
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    ok, but use x and y, because we have to plot this...

    • one year ago
  9. Falkqwer Group Title
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    ok :) 29x + 19y >_4610

    • one year ago
  10. phi Group Title
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    can you put it into slope-intercept form?

    • one year ago
  11. Falkqwer Group Title
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    IDK sorry

    • one year ago
  12. phi Group Title
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    slope intercept form is y ≥ mx + b in other words, y is by itself on the left. First step is add -29x to both sides. Just write -29x on both sides what do you get?

    • one year ago
  13. Falkqwer Group Title
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    y=x+19>_4610 IDk

    • one year ago
  14. phi Group Title
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    don't make things up. start with 29x + 19y >= 4610 write -29x on both sides: -29x + 29x + 19y >= -29x + 4610 on the left side you have 29x and -29x (think: 29 x's take away 29 x's. I get no x's) 19y ≥ -29x +4610 now divide both sides by 19. That means divide each term on both sides by 19 what do you get?

    • one year ago
  15. Falkqwer Group Title
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    y≥ -29/12x + 4610/19

    • one year ago
  16. phi Group Title
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    I assume that 12 is a typo?

    • one year ago
  17. Falkqwer Group Title
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    ohh I mean 19

    • one year ago
  18. phi Group Title
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    now, let's change into decimals (only a few digits). Roughly we get y ≥ -1.53 x + 242.6 now plot this line. Y ≥ means shade all the Y above the line. Can you plot this line?

    • one year ago
  19. Falkqwer Group Title
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    I have no idea:(

    • one year ago
  20. phi Group Title
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    for y ≥ -1.53 x + 242.6 we first plot y = -1.53x +242.6 if we set x to 0, what is y ?

    • one year ago
  21. Falkqwer Group Title
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    y ≥ 242.6

    • one year ago
  22. phi Group Title
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    Ok, x=0, y = 242.6 (0,242.6) is one point on the line can you plot this point ?

    • one year ago
  23. Falkqwer Group Title
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    idk how

    • one year ago
  24. Falkqwer Group Title
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    |dw:1358271480089:dw|

    • one year ago
  25. phi Group Title
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    yes, that looks good See http://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/coordinate-plane/v/plot-ordered-pairs if you need a refresher. now lets find y when x = 100 y = -1.53x +242.6 replace x with 100 y = -1.53*100 + 242.6 what do you get ?

    • one year ago
  26. phi Group Title
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    I picked x=100 because it is easy to multiply by 100. we could pick any x, but x near or inside our triangle makes sense.

    • one year ago
  27. Falkqwer Group Title
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    y= 395.6

    • one year ago
  28. phi Group Title
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    -1.53*100 is a negative number. try again

    • one year ago
  29. Falkqwer Group Title
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    89.6

    • one year ago
  30. phi Group Title
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    that means (100,89.6) is on the line. can you plot this point ? go to x=100 and move up about 90.

    • one year ago
  31. Falkqwer Group Title
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    |dw:1358272059574:dw|

    • one year ago
  32. phi Group Title
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    now connect the dots (or x's in this case) |dw:1358272145701:dw|

    • one year ago
  33. Falkqwer Group Title
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    d.)100 of type A; 90 of type B

    • one year ago
  34. phi Group Title
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    I shaded the area above the line, because that is where y ≥ to the line The black shaded area is everywhere where you get the needed profit (remember profit must be ≥ 4610) We also must be below the red line. To meet both requirements, we must be in the lower triangle.

    • one year ago
  35. Falkqwer Group Title
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    ahhhh ok I'm confused now...what is the answer?

    • one year ago
  36. phi Group Title
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    Once you get the "feasible" region, you check the "corners" for the (x,y) pair that matches your requirement. In this case, the bottom two spots have y=0 and the statement If you must order at least one of each type of table means we can rule out those points we have to find the intersection of the two lines. but we see by eyeball it is 100, 90

    • one year ago
  37. Falkqwer Group Title
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    so its AorD :D

    • one year ago
  38. phi Group Title
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    A is x in our graph. and B is y Here is how to find where the lines cross: you start with y= -x + 190 y = -1.53x +242.6 when they meet they have the same y values. we set -x + 190 = -1.53x +242.6 add 1.53x to both sides (you should learn how to do this, btw) 1.53x - 1x + 190= -1.53x + 1.53x +242.6 on the left we get 0.53x+190 and on the right 242.6: 0.53x +190 = 242.6 add -190 to both sides 0.53x +190-190= 242.6-190 0.53x = 52.6 divide both sides by 0.53, and x = 99.2 looking at our graph, we want x bigger than this (we have to buy a whole table) x=100 and x+y =190 replace x with 100: 100+y=190 add -100 to both sides: 100-100+y= 190-100 y=90 In a harder problem, we would use these x,y numbers in the cost equation, and find the (x,y) pair (of the three corners) that gives the lowest cost. here, we just need to find the top "corner" because the bottom 2 are ruled out by the question (we must buy some of both types, so 0 is not allowed)

    • one year ago
  39. Falkqwer Group Title
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    So the answer is A :) thank you so much for spending the time on teaching me :p I really appreciated

    • one year ago
  40. phi Group Title
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    I think you can do this stuff, but you have skimped so much in learning all the details that it is difficult to do a problem like this where you have to remember how to do lots of things: plot, solve equations, etc.

    • one year ago
  41. phi Group Title
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    Personally, I would pick just one area (example: putting equations into slope-intercept form), and watch a video at Khan

    • one year ago
  42. Falkqwer Group Title
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    ok I'll try that thanx again :)

    • one year ago
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