# MATH1003 QUANTITATIVE METHODS WITH ECONOMICS

PROJECT ASSIGNMENT
Due 11pm Sunday Week 7
Value 35%
Modules 1 and 2

 The assignment must be submitted online as a SINGLE Word file with Excel output copied and pasted (use paste special –> Excel object).
 All submissions should be typed including the mathematics in A4 page size
 All written descriptions must be in correctly structured sentences using appropriate mathematical, business and English language.
 Descriptions should be in formal language (e.g. third person ‐no use of I or me throughout).
 Figures and tables must be fully labelled and include headings.
All the information you need is given in the question or in your study material.
However if you happen to use other resources ensure that they are referenced using standard practice taught in EDUC1001.
All submitted work must be your own. Using others’ work as if it is your own can be deemed to be plagiarism.
Your assignment must be submitted online in a single word file.

Question 1 Impact of changing price upon revenue and profit
A factory worker makes teddy bears. Each teddy bear requires two (2) eyes, internal ‘stuffing’, an external body covering and four (4) paw pads. The worker uses three types of body covering – calico, corduroy and velvet. Once the teddy bears are assembled, they are distributed to toy shops for sale.
Teddy bears are assembled and sold as follows;
Calico Corduroy Velvet
Cost of body covering \$11.50 \$18.50 \$24.50
Cost of eyes (individually) \$2.50 \$2.65 \$2.75
Cost of internal ‘stuffing’ \$6.00 \$6.00 \$6.00
Cost of paw pads (per pair) \$1.85 \$2.90 \$3.60
Sale price range \$30 – \$36 \$40 – \$48 \$45 – \$55
Regardless of the materials used to make each teddy bear, there are fixed production costs of \$180. Your task is to investigate the cost, revenue and profit associated with each type of teddy bear.
Steps to complete to undertake the investigation

1. Find the total cost and total revenue functions for each type of teddy bear and plot these functions on an Excel graph (i.e. you will produce 3 graphs, each with two lines on it). For the revenue function, select a price for each teddy bear type within the price ranges in the table above.
2. Confirm the points of intersection between the cost and revenue function lines using algebra. Express your final results in co-ordinate point form: (Quantity value, Revenue value)
3. Profit will also differ for each type of teddy bear. Find the profit functions and the break-even quantity for each type.
a. Explain the meaning and significance of any points of intersection noted from steps 1 and 2 and any similarities noted from you results in step 3.
b. Discuss any differences in profitability between each type of teddy bear (for example, which teddy bear would be easiest to make a profit from?)
c. Note any assumptions you have made and any limitations of your findings.

Question 2 Impact of a price discount on revenue
A vineyard produces a range of premium white wines. One particular year, the growing conditions for white wine grapes are particularly good, leading to excessive white wine production above what would normally be expected. As warehouses and bottle shops which store and then sell this particular wine have limited capacity, the vineyard needs to clear this excess stock and does so by reducing the average price of each bottle of wine by \$9 per bottle.
Your task is to determine the consequences of the \$9 price reduction.
The supply and demand equations are given by
Demand Equation: 𝑝 = 144 − 11𝑎𝑞
Supply Equation: 𝑝 = 0.000025𝑞
2 + 6𝑏𝑞 + 25
where
q is the number of customers (in hundreds per year) ;
p is the price of a bottle in dollars.
a and b are coefficients to be chosen below.

Steps to complete to undertake the investigation

1. Obtain two random numbers for a and b between 0.1 and 0.9 inclusive. Use the Excel random
function =Rand() or the RANDOM key on your calculator.
2. Find the equilibrium price and quantity algebraically, without the price decrease.
3. Update the demand equation to include the \$9 price decrease.
4. Use algebra to find the new equilibrium price and quantity.
5. Use Excel to graph on the same set of axes, the original supply and demand equations (from part 1)
and the updated demand equation with the proposed price decrease (part 3)
6. Use your results to complete the following summary table. Round answers to two decimal places, except for total revenue amounts which round to 0 decimal places

a. Discuss the effect of the surcharge on price, quantity and revenue
b. Provide a recommendation to the vineyard on whether to proceed with the price
decrease or not
c. Note any assumptions you have made and any limitations of your findings.

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