algebra math 123

Question

A company can manufacture x hundred items for a total cost of C = 300 + 1100 x − 100 x 2 . Find x if the total cost is $ 2 , 100 .

Answer 1

Rewriting:

-100x²+1100x+300 = 2100

-100x²+1100x-1800 =0

divide both sides by -100

x^2-11x+18=0

Factoring

(x-9)(x-2) = 0 x = 9, 2

C(9) = 300+9900-8100 = 2100

C(2) = 300+2200-400 = 2100

Probably to make the most profit from selling the items, making 9 hundred items is the better choice.

Answer 2

Hello!

Hmm, I'm assuming that equation is C = 300 + 1100x - 100x², right?

First thing to do would be to divide both sides by 100, just makes things easier:

If C = 2100,

then 21 = 3 + 11x - x²

which is: -x²+11x +3 = 21

which is: -x²+11x - 18 = 0

now multiply both sides by -1 to make it look nicer:

x²-11x + 18 = 0

Isn't that a better equation to deal with? Now, let's solve for the solutions for x:

x²-11x + 18 = 0

(x-9)(x-2) = 0

Therefore x = 9 OR x = 2.

Now, remember what the question is asking for...Hope this helps!