Question

The demand for plastic brownie dishes is given below where q represents the number of brownie dishes that can be sold at a price of p
q(p)=363609-(p+1)^2

1. Use q(p) to determine the lowest price at which it will be unable to sell any dishes

(basically what formula do I need to use to solve this?)

Answer 1

sorry idk

Answer 2

Set the equation equal to 0, because q(p) is how many dishes can be sold at a certain price, and you want to find the price where you can sell 0 dishes (no dishes)

Answer 3

okay leme try

Answer 4

Set the equation equal to 0, because q(p) is how many dishes can be sold at a certain price, and you want to find the price where you can sell 0 dishes (no dishes)

Answer 5

would it start out like 363609=(p+1)^2? or should i simplify out the (p+1)^2 to p^2+2p+1?

Answer 6

Yes, expand it into a quadratic equation and solve it as you would

Answer 7

so it would be 363609=p^2+2p+1?

Answer 8

and then solve for p?

Answer 9

Move all the terms over to one side first and set it equal to 0

Answer 10

-p^2+2p=363608?

Answer 11

No, 0 = p^2 + 2p - 363607

Answer 12

would that be the answer then?

Answer 13

Wait, let me check the original equation first

Answer 14

\[ 0 = 363,609 - (p+1)^2 = 363,609 - p^2 + 2p + 1 = p^2 - 2p - 363,610\]

Answer 15

so 0=p^2-2p-363610?

Answer 16

how would i solve for p then sense it is in two separate forms?

Answer 17

You can use the quadratic equation, and the price should be a positive number

Answer 18

[2\pm \sqrt{1454444}/2\]?

Answer 19

\[2\pm \sqrt{1454444}/2\]?

Answer 20

\[\frac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(-363,610)}}{2(1)} = \frac{2 \pm \sqrt{4 - (-1,454,440)}}{2} = \\ \frac{2\pm \sqrt{1454444}}{2} = 1\pm \sqrt{363,611}\]
And 1 - sqrt(363,611) is going to be negative so you choose the 1+ sqrt(363,611) value as 'p'

Answer 21

so your saying the answer would be 604 then?

Answer 22

Rounded, yes

Answer 23

its saying that isnt correct ;/

Answer 24

Let me look back

Answer 25

Does the question say \[q(p) = 363,609 - (p + 1)^2\] or \[q(p) = 363,609 \cdot -(p + 1)^2\]

Answer 26

the first one u put

Answer 27

In any case, for the first one, I think I made an error in sign distribution while I was typing it...I worked it out on paper and it came out differently; the solutions are -604 and 602 so it's 602 to satisfy the original equation

Answer 28

correct thank you so much!