A farmer wants to make a rectangular field with a total area of 200 m2. It is surrounded by a fence. It is divided into 3 equal areas by fences. What is the shortest total length of fence with which this can be done? A manufacturer wishes to make tee-shirts for the band Indigo Girls. They sell for 15 dollars each. She must deliver all the tee-shirts in 20 days time. The manufacturer will first set up some machines. Once all machines are set up she will turn them on. Each machine takes one day to set up. A machine produces 200 tee-shirts in one day. All the machines must be set before any of them are turned on.

(a) Express the amount of money she will receive for the shirts in terms of the number of machines m she decides to set up.

(b) Use calculus to find out how many machines she should set up to obtain the most money.
A commuter railway has 800 passengers per day and charges each one two dollars per day. For each 1 cents that the fare is increased, 5 fewer people will go by train. What is the greatest profit that can be earned?
A poster is to have a total area of 245 cm2. There is a margin round the edges of 6 cm at the top and 4 cm at the sides and bottom where nothing is printed.

What width should the poster be in order to have the largest printed area?