Assignemnt

1. If the population of a Fantasy Island is growing at 2% per year and if its population in the year 2006 was 2,200,000.

a. Determine an exponential equation representing its population as a function of time.

b. Determine its population in 2020.

c. Determine what was its population in 2004.

2. The demand and supply equations for a good are given as q² + 8q + 220 = 11p and q²+ 6q - 384 + 12p = 0 respectively, where q is the quantity demanded and supplied and p is the price.

a. Find the equilibrium price and quantity of the good.

b. Determine the revenue function of the good.

c. Hence, or otherwise determine the revenue level at the market equilibrium, to the nearest whole number.

3.

i. If the region shaded green in the diagram above represents a solution set, list the system of inequalities which define that region, if it is possible. Provide working to support your answer.

4. A farmer has 300 square metres of land suitable for cultivating the crops baigan, bodi, and pumpkin. The cost per square metre of cultivating baigan, bodi, and pumpkin is $20, $60, and $70, respectively. The farmer has $13,350 available for land cultivation. Each square metre of baigan requires 10 hours of labour time, each square metre of bodi requires 35 hours, and each square metre of pumpkin requires 30 hours. The farmer has a maximum of 6525 hours of labour time available. If he desires to plant his entire plot of land, use the entire budget, and all the labour time available:

a. Derive a system of three equations in x, y and z, where x is the number of square metres of baigan, y is the number of square metres of bodi, and zis the number of square metres of pumpkin planted.

b. Use the inverse method to derive, how many square metres of each crop should he plant?

5.

i. If the profit derived from producing x hundred units of a commodity is

P = 4000 (x - 2) (15 - x) dollars.

a. Find P'(x).

b. Determine the level of output at which P'(x) = 0.

c. What is the economic significance of the level of production determined in part (b) above?

ii. If x thousand dollars is spent on advertising brush cutters the amount of brush cutters sold will be determined by the function

125 517

B(x) = 2300 + (125/x) - (517/x²);   for 3 ≤ x ≤ 12

a. At what rate will sales be changing when $6000 is spent on advertising?

b. At what rate will sales be changing when $9000 is spent on advertising?

c. 9 Are sales increasing or decreasing for the level of advertising expenditure in parts (a) and (b) above?