Chapter $16$ Problems & Applications

$6.$ Problems and Applications Q$6$

You live in a town with $300$ adults and $200$ children, and you are thinking about putting on a play to entertain your neighbors and make some money.

A play has a fixed cost of $$1,000,$ but selling an extra ticket has zero marginal cost. Here are the demand schedules for your two types of customers:

$\backslash$table$[[\backslash$table$[[$Price$],[($Dollars$)]],\backslash$table$[[$Adults$],[($Tickets$)]],\backslash$table$[[$Children$],[($Tickets$)]]],[10,0,0],[9,50,0],[8,100,0],[7,150,0],[6,200,0],[5,250,50],[4,300,100],[3,300,150],[2,300,200],[1,300,200],[0,300,200]]$

To maximize profit, you would charge $$ for an adult's ticket and $$ for a child's ticket. Total profit in this case would be

$$

The city council passes a law prohibiting you from charging different prices to different customers.