a.  revenue $200/person (50 min.). b.  >50 (max. of 80 people), rate/person reduced by $2. c.  cost $6000 fixed plus $32 per person.  # people to max profit?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The revenue per person is $200 for 50 minutes. If the number of persons is greater than 50 but less than 80 the revenue earned per person is reduced by $2 to $198. For x number of people the cost incurred is $6000 + 32*x

If the number of people x is `x <= 50` , the profit earned is $200*x - 6000 - 32*x = -6000 + 168*x and for `80 >= x >50` , the profit earned is 198*x - 6000 - 32*x = -6000 + 166*x

From the expressions for profit derived earlier it is seen that as the number of people increases there is an increase in profit as -6000 is a constant and both of 168*x and 166*x are always positive.

For x = 50, the profit earned is $2400 and for x = 80, the profit earned is $7280.

The number of people to maximize profit is 80.

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial Team