p(x)=2-(100/x)

Question

The fixed cost is $20 (you have to pay the RA to keep him from reporting you to the IRS), the marginal cost is $0.05 per cookie. At the beginning of your first run, you priced your cookies at $2.00 per cookie and realized no one was buying. So, you lowered the price and noticed the relationship between the price per cookie p(x) and the number of cookies sold x was p(x)=2−(100/x)

Answer 1

p=2-100/x

2 -p = 100/x

x = 100/(2-p)

$2 price does not mean no one buys the cookies

at price= near $2, an infinite number of cookies are sold or

x=100/(2-2) = 100/0 = undefined, an indeterminate number as 0x=0, 0x never =100, unless x = infinity

at price =$1, 100/(2-1) = 100 cookies sold

at price = $3, 100/(2-3) = -100 cookies "sold" as people try to give back and get refunds for cookies already purchased

revenue=r =px = x(2- 100/x) = 2x -100

cost=c= 20+.05x

Profit =P = r-c = 2x-100 -20 -.05x

= 1.95x -120

break even point = x= 120/1.95 =about 61.54

sell 62 cookies and you make a small profit

sell 61 cookies and you make a small loss

the more cookies you sell the larger the profit, theoretically if p=2-100/x is the model, but the model doesn't account for limited number of consumers or limited number of cookies each consumer would want