I have the following problem that asks 3 questions...
4. A charter flight company has variable pricing for its tickets. When exactly 200 people fly, then the cost is $300 per person. Whenever more than 200 people fly, the cost is reduced by $1 per person. Let x be the number of people beyond 200 that fly. Assume that there are always at least 200 people.
a. The total number of people who fly will be 200 + x. The revenue from each person will be 300 – x. Using these quantities, what is the total revenue the company can expect from all the passengers?
b. What number of passengers will maximize revenue for the company? Show your work and explain your answer.
c. What price does each passenger pay at this maximum revenue point?
For part a. I believe that the equation for total revenue would be -x^2 + 100x +60,000. I came up with this by taking (200 + x) (300-x). It seems that this is incorrect to me though. Also, I'm not sure how to find out the number of passengers. Once I find out the number of passengers then I would be able to find out how much they each pay.
4. A charter flight company has variable pricing for its tickets. When exactly 200 people fly, then the cost is $300 per person. Whenever more than 200 people fly, the cost is reduced by $1 per person. Let x be the number of people beyond 200 that fly. Assume that there are always at least 200 people.
a. The total number of people who fly will be 200 + x. The revenue from each person will be 300 – x. Using these quantities, what is the total revenue the company can expect from all the passengers?
b. What number of passengers will maximize revenue for the company? Show your work and explain your answer.
c. What price does each passenger pay at this maximum revenue point?
For part a. I believe that the equation for total revenue would be -x^2 + 100x +60,000. I came up with this by taking (200 + x) (300-x). It seems that this is incorrect to me though. Also, I'm not sure how to find out the number of passengers. Once I find out the number of passengers then I would be able to find out how much they each pay.
