# 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 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.

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