Question

A company's monthly profit, P, from a product is given by P = −x2 + 105x − 1050, where x is the price of the product in dollars. What is the lowest price of the product, in dollars, that gives a monthly profit of $1,550?

Answer 1

substitute $1550 for P then just factor out the equation o.0

Answer 2

so 1550 = -x^2 + 105x - 1050? And then do i factor -x^2 + 105x - 1050?

Answer 3

yep :D

Answer 4

the you would get two zeros so pick the one with the least value and also it cannot be negative

Answer 5

then*

Answer 6

wait what?! :o

Answer 7

wait hold on....
is the original equation P = −x2 + 105x − 1050?

Answer 8

yes

Answer 9

then the equation you need to factor out is −x2 + 105x − 2100=0

Answer 10

ah well just solve it out with whatever method you want and tell me what you get

Answer 11

but no factors of -2100 are the sum of 105? i think..

Answer 12

do you know what the answer is? @alexwee123

Answer 13

May I help you ??

Answer 14

yes please :)

Answer 15

You have given P = 1550:
Plug this value in:

\(1550 = -x^2 + 105x - 1050\)

So:

\(x^2 - 105x + 2600 = 0\)

You have to solve this quadratic equation..

Answer 16

Here a = 1, b = -105 and c = 2600

Find Discriminant here:

\(D = b^2 - 4ac\)

\(D = 11025 - 10400\) = ??

Answer 17

So you will get like 625 after subtracting them right ??

Answer 18

\[D = 625 \implies \sqrt{D} = 25\]

Right ??

Answer 19

yes correct!

Answer 20

oh well i factored the equation x^2 - 105x + 2600 = 0 and got
(x - 65) ( x - 40?

Answer 21

(x - 65) ( x- 40)

Answer 22

I did the method where you take the factors of 2600 that are the sum of -105

Answer 23

Great well done..

Answer 24

\[(x-65)(x-40) = 0\]

So,

x = 65 and x = 40 you will get..

Answer 25

i'm confused :o

Answer 26

How ??

Answer 27

oh no okay i understand! did you make x - 65 = 0 and x - 40 = 0? Then you get x = 65 and x = 40 right?

Answer 28

Yes I did the same..

Answer 29

oh ok so then is the final answer 40?! :o

Answer 30

Yes it is..

Answer 31

ok thank you :D