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:
where is the Fuel Tank
capacity of the aircraft in liters and $F$ is the amount of
fuel already consumed in liters. A A380's 10 fuel tanks can
hold a maximum of
L 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 with
L in its tanks? 2.Let us explore a simple example of the Free Rider problem:
Suppose that you and 2 of your friends go to Doyle’s
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 $35.80
and $52.60 each. Suppose that your utility function is given
by the following function:
where is 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
maximizes your net utility (i.e. Utility less cost)? 3.Find the area between the graphs of
between
and
. 4.What is the element
function: and of the Hessian matrix for the evaluated at . 5.Find the rate of change of the following function at
given the following information:
and
6.Suppose we have the following implicit function:
Find the value of the second derivative at .
. 7.At which point in its positive domain (i.e.
) does the
tangent to the following curve have its greatest (positive)
slope
?
8.Evaluate the following definite integral:
9.Evaluate at for the function: 10. For the function
to the curve at
. , find the slope of the tangent

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