1 Suppose, for modelling simplicity, that an aircraft's fuel burn rate (i.e. the rate at which it consumes fuel over time) decreases the longer the aircraft flies. This occurs because the aircraft burns fuel relative to the weight it carries. Using fuel means less fuel now required to keep a lighter weight aloft. Suppose that an A380's fuel consumption rate can be described by:

whereis the Fuel Tank capacity of the aircraft in litres and $F$ is the amount of fuel already consumed in litres.

A A380's 10 fuel tanks can hold a maximum ofL but it does not necessarily start every flight with full tanks (i.e.is not necessarily true). Suppose. What is the rate of fuel burn when the A380 has flown for 4hours if the A380 began its flight withL in its tanks?

2 Let us explore a simple example of the Free Rider problem:

Suppose that you and 5 of your friends go to Doyles Seafood at Watsons Bay for lunch. As a group, you decide to order one main each and share the food. You also decide to split the bill evenly.Mains cost between $37.41 and $58.95 each. Suppose that your utility function is given by the following function:whereis the total value of food ordered.

Supposing that your friends follow your lead and order mains of equivalent value to the one you order, what is the price of the main (call this) which maximises your net utility (i.e. Utility less cost)?

(Give your answer to 2 decimal places