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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- anonymous

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- anonymous

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

- anonymous

please help you guys :/ I really need it.

- Hero

I've seen this question before.

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## More answers

- anonymous

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

- anonymous

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

- Hero

Okay, hang on

- anonymous

Thanks (:

- anonymous

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

- anonymous

it's alright thanks for taking the time (:

- anonymous

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

- anonymous

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

- 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

- anonymous

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

- 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

- anonymous

er man, I'm terrible at this..

- Hero

Wow you figured it out

- anonymous

oh did I O.o

- anonymous

That seemed so long and complicated x.x

- Hero

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

- Hero

I already posted my steps

- anonymous

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

- Hero

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

- anonymous

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

- Hero

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

- anonymous

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

- anonymous

After trying and failing miserably, But I do think there's a quicker way :/ Just can't think of what it is at all :/

- Hero

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

- anonymous

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

- anonymous

oh goodness... haha yeh I guess, so how shall I go about this second question?

- Hero

Well from looking at the answers, it will be either A or D. And if I had to guess, I would guess A

- Hero

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

- Hero

without doing any work

- anonymous

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

- anonymous

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)

##### 1 Attachment

- anonymous

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

- Hero

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

- Hero

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

- Hero

There's one obvious one that works

- 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?

- anonymous

Sorry I was in the shower O.o

- anonymous

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

- anonymous

The...first one lol?

- anonymous

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

- anonymous

You must be doing something now lol...

- Hero

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

- anonymous

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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