2306AFE - Quantitative Methods for Business, Finance and Economics - Accounting & Finance Assignment Help

Assignment Task

QUESTION-1
(a) Solve the equation -
5xx -2 = 5xx + 2 ?

(b) The demand function for Coke is given as follows:
Q = 40 - 5P, Calculate the price elasticity of demand at Q = 5.

QUESTION-2:
Find the sum of the first n terms for the geometric progression series.
(a) a = 2, r =-1, n is an odd integer
Where a denotes the first term, r the common ratio, and n the number of terms.

(b) Find the sum to n terms of the following series -
7 + 77 + 777 + …… to n terms.

QUESTION-3:
A mobile phone company charges a fixed price of $48 for each mobile phone sold. It is assumed that there is no fixed cost. The total cost (TC) function of the company is given as follows:
TC =44Q – 6Q2 + 4Q3 Write the equation for total revenue. Find the break-even level of output.

QUESTION-4:
(a) Find the present value of a 10-year annuity of $8000 per annum, given the interest rate of 6% for the first year, 7% for the second year, 8% for the third year, 9% for the fourth year, and 10% for the rest of the period.

(b) Lisa wishes to accumulate $10000 over 5 years for an overseas trip. She will make a deposit every 6-months, and the funds will earn the interest rate of 4% per annum compounded semi-annually. How much should Lisa deposit every 6-months (that is, twice a year)?

(c) A Motorbike firm plans to expand its business and, thus, invest in a new project. The “Initial Cost” on and the expected future “Net Cash Flows” from Project A and Project B are given in the table below.
Item Project A Project B
Initial Cost 20000 20000
Net Cash Flows
Year 1 1000 -2000
Year 2 3000 4000
Year 3 8000 10000
Year 4 12000 14000
Year 5 16000 20000
Use the Net Present Value (NPV) method to determine which of the two projects the firm should choose to invest in, if the rate of interest is 5% per annum.

QUESTION-5:
A car company has the following total cost (TC) and total revenue (TR) functions:
TC = 14Q4 - 2Q3 + 10Q2 + 200Q + 5000 TR = Q(6Q + 200)
The company maximizes its profits when marginal cost is equal to marginal revenue. Find the profit-maximizing level of output.

QUESTION-6:
A firm may sell its product in two different markets. The demand functions for these markets are given as follows:
Market I:
Market II:
The total cost function of the firm is given by the equation:

where P is the price in dollars, Q the quantity in units, and TC the total cost in dollars.
(a). Find the price which should be charged in each market to maximize firm’s profit (2 Marks).

(b). Find the price elasticity of demand when profit is maximized in each market

QUESTION-7:
A food producer has two processing plants, P1 and P2, in New South Wales. The producer operates 5 days a week. The cost of running plant P1 is $3000 per day. The cost of running plant P2 is $2000 per day. After processing, food is graded into three grades: Grade I, Grade II and Grade III. The producer has contracted to provide each week the following quantities to the bulk buyer.
Grade I: 200kg
Grade II: 200kg
Grade III: 300kg
Each day, plant P1 processes 100kg of Grade 1, 160kg of Grade II and 100kg of Grade III food. The corresponding quantities for plant P2 are 100kg, 50kg and 300kg, respectively. The objective of the producer is to fulfil the contract with a minimum cost.
Use the information given above and set up the linear programming (LP) problem.
Using the linear programming problem, you have set up, answer the following questions:
? Calculate and plot all the constraints and clearly shade the feasible region. Clearly mark and label all the constraints and corner point solutions on the graph. Show all the workings and calculations.
Calculate the cost minimizing number of days for which each plant should be operated per week to fulfil the contract? (fractional days allowed).
What is the minimum cost the food producer incurs?
* Cost minimizing number of days =
* Minimum cost =

QUESTION-8:
Supply and demand functions of a product are given as follows:
Where p is the price in dollars, Qd is the quantity demanded in units, and Qs is the quantity supplied in units.
(a) Algebraically, find the equilibrium price and quantity

(b) Now, suppose the government has imposed an indirect sales tax of $100 per item on the product. Find the new equilibrium price and quantity after the tax. What is the effect of tax on the price charged and the quantity traded in the market?

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