Catering a dinner: You are having a dinner catered. You pay a rental fee of $150 for the dining hall, and you pay the caterer $10 for each person who attends the dinner. a. Suppose you just want to...

Catering a dinner: You are having a dinner catered. You pay a rental fee of $150 for the dining hall, and you pay the caterer $10 for each person who attends the dinner.

a. Suppose you just want to break even.

i. How much should you charge per ticket if you expect 50 people to attend?

ii. Use a formula to express the amount you should charge per ticket as a function of the number of people attending. Be sure to explain the meaning of the letters you choose and the units.

iii. You expect 65 people to attend the dinner. Use your answer to part ii to express in functional notation the amount you should charge per ticket, and then calculate that amount.

b. Suppose now that you want to make a profit of $100 from the dinner. Use a formula to express the amount you should charge per ticket as a function of the number of people attending. Again, be sure to explain the meaning of the letters you choose and the units.