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MeganDarling

  • 2 years ago

Your computer-supply store sells two types of inkjet printers. The first, type A, costs $237 and you make a $22 profit on each one. The second, type B, costs $122 and you make a $19 profit on each one. You can order no more than 120 printers this month, and you need to make at least $2,400 profit on them. If you must order at least one of each type of printer, how many of each type of printer should you order if you want to minimize your cost? Possible answers: 69 of type A : 51 of type B 40 of type A : 80 of type B 51 of type A : 69 of type B 80 of type A : 40 of type B

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  1. MeganDarling
    • 2 years ago
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    2.A factory can produce two products, x and y, with a profit approximated by P = 14x + 22y – 900. The production of y can exceed x by no more than 200 units. Moreover, production levels are limited by the formula x + 2y ≤ 1600. What production levels yield maximum profit? x = 400; y = 600 x = 0; y = 0 x = 1,600; y = 0 x = 0; y = 200

  2. MeganDarling
    • 2 years ago
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    please help you guys :/ I really need it.

  3. Hero
    • 2 years ago
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    I've seen this question before.

  4. MeganDarling
    • 2 years ago
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    :o oh haha? Well it must have been someone from my same school then I suppose

  5. MeganDarling
    • 2 years ago
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    But I really need help I've been asking these same questions for about 3 days and no one has helped :/

  6. Hero
    • 2 years ago
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    Okay, hang on

  7. MeganDarling
    • 2 years ago
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    Thanks (:

  8. MeganDarling
    • 2 years ago
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    Hmm :o I'll wait longer haha these aren't easy questions!

  9. MeganDarling
    • 2 years ago
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    it's alright thanks for taking the time (:

  10. MeganDarling
    • 2 years ago
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    Man..I would have taken like a year to do it then O.o

  11. MeganDarling
    • 2 years ago
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    it's alright haha you don't have to do the second one if it's going to take you too long x.x I don't wanna waste more of your time haha I feel bad, like other people need you :o

  12. Hero
    • 2 years ago
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    If we let: a = number of type A computers b = number of type B computers Then we can produce the following equations: Amount of Computers a + b ≤ 120 Cost of Computers: C(a,b) = 237a + 122b Profit from computers: 22a + 19b ≥ 2400

  13. MeganDarling
    • 2 years ago
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    So hmm, would it be 40 of type A and 80 of B ? x.x I'm just sorta guessing here

  14. Hero
    • 2 years ago
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    So now we take the amount equation and the profit equation and solve for a and b: a + b ≤ 120 22a + 19b ≥ 2400 Multiply the first equation by 22 to get: 22a + 22b ≤ 2640 22a + 19b ≥ 2400 Isolate 22a in both equations: 22a ≤ 2640 - 22b 22a ≥ 2400 - 19b Now set: 22a ≤ 22a 2400 - 19b ≤ 2640 - 22b Place like terms on the same side: 22b - 19b ≤ 2640 - 2400 3b ≤ 240 b ≤ 240/3 b ≤ 80 Thus a ≤ 40 since we know that a + b ≤ 120

  15. MeganDarling
    • 2 years ago
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    er man, I'm terrible at this..

  16. Hero
    • 2 years ago
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    Wow you figured it out

  17. MeganDarling
    • 2 years ago
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    oh did I O.o

  18. MeganDarling
    • 2 years ago
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    That seemed so long and complicated x.x

  19. Hero
    • 2 years ago
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    I'm trying to figure out what you did, lol

  20. Hero
    • 2 years ago
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    I already posted my steps

  21. MeganDarling
    • 2 years ago
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    I just guessed to be honest I'm kind of a lucky guesser x.x

  22. Hero
    • 2 years ago
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    I think you did some plug and play to figure it out. You already had answer choices.

  23. MeganDarling
    • 2 years ago
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    I really should learn how to do it though since I can't guess right every time haha

  24. Hero
    • 2 years ago
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    I, on the other hand, figured it out the hard way. It was very toilsome.

  25. MeganDarling
    • 2 years ago
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    I really didn't lol I just sat and stared at the answers for while.. x.x

  26. MeganDarling
    • 2 years ago
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    After trying and failing miserably, But I do think there's a quicker way :/ Just can't think of what it is at all :/

  27. Hero
    • 2 years ago
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    Believe it or not, what I posted IS the easy way. Good luck finding an easier way.

  28. MeganDarling
    • 2 years ago
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    Haha well your really good at math and I'm super jealous >.< But I appreciate the work!

  29. MeganDarling
    • 2 years ago
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    oh goodness... haha yeh I guess, so how shall I go about this second question?

  30. Hero
    • 2 years ago
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    Well from looking at the answers, it will be either A or D. And if I had to guess, I would guess A

  31. Hero
    • 2 years ago
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    Matter of fact, I'm just going to say the answer is A

  32. Hero
    • 2 years ago
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    without doing any work

  33. MeganDarling
    • 2 years ago
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    Your guess is better than mine haha! I'll try it I suppose .

  34. MeganDarling
    • 2 years ago
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    Graph the system of constraints and find the value of x and y that maximize the objective function. Objective function: C = 7x – 3y (2.5, 2.5) (0, 2) (0, 0) (5, 0)

  35. MeganDarling
    • 2 years ago
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    Any ideas on this one? It's the last one I have no idea about :/ ?

  36. Hero
    • 2 years ago
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    Well basically we have to find the coordinates the yield the maximum value of C. This is an easy one too.

  37. Hero
    • 2 years ago
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    All you have to do is just plug the values into the formula

  38. Hero
    • 2 years ago
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    There's one obvious one that works

  39. Hero
    • 2 years ago
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    c'mon Megan, think outside the box. Which set of coordinates can you plug into the function to yield the highest value of C?

  40. MeganDarling
    • 2 years ago
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    Sorry I was in the shower O.o

  41. MeganDarling
    • 2 years ago
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    Nothing is ever easy for me :P Math is like a foriegn language to me :/

  42. MeganDarling
    • 2 years ago
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    The...first one lol?

  43. MeganDarling
    • 2 years ago
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    er the 4th one ... erm, I'm so dumb x.x

  44. MeganDarling
    • 2 years ago
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    You must be doing something now lol...

  45. Hero
    • 2 years ago
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    Yes, it is the 4th one. (5,0)

  46. MeganDarling
    • 2 years ago
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    ah, that's what I thought :P But I just didn't know for sure x.x I didn't really give that question much thought I guess haha

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