## MeganDarling 3 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

1. MeganDarling

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

3. Hero

I've seen this question before.

4. MeganDarling

:o oh haha? Well it must have been someone from my same school then I suppose

5. MeganDarling

But I really need help I've been asking these same questions for about 3 days and no one has helped :/

6. Hero

Okay, hang on

7. MeganDarling

Thanks (:

8. MeganDarling

Hmm :o I'll wait longer haha these aren't easy questions!

9. MeganDarling

it's alright thanks for taking the time (:

10. MeganDarling

Man..I would have taken like a year to do it then O.o

11. MeganDarling

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

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

So hmm, would it be 40 of type A and 80 of B ? x.x I'm just sorta guessing here

14. Hero

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

er man, I'm terrible at this..

16. Hero

Wow you figured it out

17. MeganDarling

oh did I O.o

18. MeganDarling

That seemed so long and complicated x.x

19. Hero

I'm trying to figure out what you did, lol

20. Hero

21. MeganDarling

I just guessed to be honest I'm kind of a lucky guesser x.x

22. Hero

I think you did some plug and play to figure it out. You already had answer choices.

23. MeganDarling

I really should learn how to do it though since I can't guess right every time haha

24. Hero

I, on the other hand, figured it out the hard way. It was very toilsome.

25. MeganDarling

I really didn't lol I just sat and stared at the answers for while.. x.x

26. MeganDarling

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

Believe it or not, what I posted IS the easy way. Good luck finding an easier way.

28. MeganDarling

Haha well your really good at math and I'm super jealous >.< But I appreciate the work!

29. MeganDarling

30. Hero

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

Matter of fact, I'm just going to say the answer is A

32. Hero

without doing any work

33. MeganDarling

Your guess is better than mine haha! I'll try it I suppose .

34. MeganDarling

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

Any ideas on this one? It's the last one I have no idea about :/ ?

36. Hero

Well basically we have to find the coordinates the yield the maximum value of C. This is an easy one too.

37. Hero

All you have to do is just plug the values into the formula

38. Hero

There's one obvious one that works

39. Hero

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

Sorry I was in the shower O.o

41. MeganDarling

Nothing is ever easy for me :P Math is like a foriegn language to me :/

42. MeganDarling

The...first one lol?

43. MeganDarling

er the 4th one ... erm, I'm so dumb x.x

44. MeganDarling

You must be doing something now lol...

45. Hero

Yes, it is the 4th one. (5,0)

46. MeganDarling

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