How do I write this?

Question

Sam charges ten dollars for a one year subscription to his on-line newsletter. Sam currently has 600 subscribers and he estimates that for each $1 decrease in the subscription price, he would gain 100 new subscribers.

a. Write the equation in factored form to model this situation.

Answer 1

for $10 600 customers

for $9 700 customers

one dollar decrease adds 100 customers

it's linear relation

slope = change in customers over change in price = 700-600)/9-10)= -100

y intercept = b

y =-100x +b plug in either point to solve for b

600 = -100(10) +b

b = 1600

y = -100x+1600

or

C = -100p + 1600 where x or p = price, y or C = number of customers

at $16, no one shows up, zero customers

real question is what is the revenue or profit maximizing price??

$35? midway in quadrant 1, between $0 and $16

Revenue = pC = -100p^2 +1600p = R

R' =- 200p +1600 = 0

p = 1600/200 =$8 Bingo

He needs to drop his price to $8, he'll gain 200 customers, up to 800

but make more money, if that's his goal, making 8x800 = $6400

while now he "just" makes 10x600 = $6000, $400 less than he could make