WECO1031 Term 4 2022 Assignment Questions – Version A

1. (5 marks) Suppose Delta Corp allocates $600,000 to spend on research and marketing. Delta Corp
estimates that by spending $ on marketing and $ on research it will sell a total amount of ()
(measured in $):
= 304513

Using Lagrange multipliers calculate the optimum amount that Delta Corp should spend on marketing
and research to maximise sales?



2. (5 marks) Suppose the demand function of a candy business () is given by
= 1000 −0.2
where:
=
The fixed costs of the candy business are $100, and the variable costs are $2 per unit. Calculate the
unit price of candy that maximises the profit of the candy business.



3. (5 marks) Suppose Australia’s aggregate income () has two components: aggregate consumption ()
and aggregate investment (). In year :



= 0.5 ( + − )
= 0.7 + 500
= 0.2 + 500
Using differential equations, find an expression for ( ) ℎ (0) = 15,000.