Applications of derivatives: maximizing area and revenue

4. A Norman window consists of a rectangle with a semi-circle mounted on top (see the figure). What are the dimensions of the Norman window with the largest area and a fixed perimeter of P meters?

5. A bus company will charter a bus that holds 50 people to groups of 35 or more. If a group contains exactly 35 people, each person pays $60. In larger groups, everyone's fare is reduced by $1 for each person in excess of 35.

(a) What is the revenue, if the bus is chartered to 35 people? 36 people?
37 people?
(b) Find a formula for the revenue in terms of the number of people
chartering the bus.
(c) Determine the size of the group(s) for which the bus company's
revenue will be the greatest.
(Note: you need to check that your answer makes physical sense and
that it is correct as the physical constraints allow.)

It composed of two applications of derivative problems: maximizing the area with a fixed perimeter and maximzing the revenue of a bus company. The solution is well presented and detailed.

Please see attached file for full problem description.
The revenue derived from the production of x units of a particular commodity is million dollars. What level of production results in maximum revenue? What is the maximum revenue?
a. a. Maximum at x = 8 and maximum revenue is R(8) = 32 (million dollars)
b. b. Maxi

A farmer has 480 meters of fencing. He wishes to enclose a rectangular plot of landand to divide the plot into three equal rectangles with two parallel lengths of fence down the middle. What dimensions will maximize the enclosed area? Be sure to verify that you have found the maximum enclosed area.

A. Write a function for your profits for each price you charge. This is done by multiplying (P-.5) times your function (y= -100x + 250). I.e. if your function is Cups Sold = 1000 - 100P, your profit function would be (P - .5)*(1000 - 100P).
B. Calculate the first derivative of your profit function, and create another table

See attached file
1. Refer to the above data. At the profit-maximizing output the firm's total revenue is:
A. $48.
B. $32.
C. $80.
D. $64.
Marginal Marginal
Output revenue cost
0

Please can you give some ideas on how to solve the problem, even if you can't help with the final solution..Thank you!
The demand for bus transportation in a small city is P=100-Q, where P is the price of the bus fare, and Q are rides per month (units=10,000 rides).
(a) What is the revenue function for bus rides? Plot this

A new competitor enters the industry and competes with a second firm, which had been a monopolist. The second firm finds that although demand is not perfectly elastic, it is now relatively more elastic. What will happen to the second firm's marginal revenue curve and to its profit maximizing price?

2) A piece of paper for a poster contains 1000 cm^2. The margins at the top and bottom are 9cm and the side margins are 6 cm. What are the dimensions of the sheet if the printed area is to be a maximum.
Answers 2root3 and 3root3
3) At 9am ship B was 65km due east of ship A. Ship B was then sailing west at 10km/h and A was s