**Please follow these guidelines for the assignment.**

- The assignment must be submitted online as a single word file with excel output copied and pasted.
- All submissions should be typed including the mathematics in A4 size.
- All written descriptions must be correctly structured sentences using appropriate mathematical, business and English language
- Description should be formal language
- Figures and tables must be fully labelled and include headings.

## Task: MAT10706 Quantitative Methods With Economics Assignment

**Question 1 Impact of changing price upon revenue and profit**

A factory worker assembles small hand held electronic devices . Smartphones are the most popular item assembled. Each smartphone requires electronic parts and an outer casing . The worker uses 3 brands of electronics parts – Copper, silicon and Platinum. Once the smartphones are assembled , they are distributed for sale. Smartphones are assembled and sold as follows.

In addition to this above, there are also fixed production costs of $600 for Copper, $800 for Silicon and $1200 for Platinum.

Your task is to investigate the cost , revenue and profit associated with each type of smartphone.

Steps to complete to undertake the investigation:

- Find the total cost and total revenue functions for each type of smartphone and plot these functions on excel graph.(i.e. you will produce 3 graphs, each with 2 lines). For the revenue function, select a price for each smartphone within the price ranges in the table above.
- Find the points of intersection between the cost and revenue function lines using algebra.
- Profit will also differ for each smartphone. Find the profit functions and the brake even point for each smartphone.
- Summerise your findings in 200 words.a. Explain the meaning and significance of any point of intersection.b. Discuss any differences in profitability between each type of smartphone(pay particular attention to the break even point).c.Note any assumptions you have made and any limitations of your findings.

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**Question 2 Impact of price discount on revenue**

A restaurant in a sea side town is renowned for its lunch menu seafood. One year, the local fishing catch is higher than usual. To clear the excess stock of seafood, the restaurant reduces the average price of its lunch. The restaurant manager reduces the lunch price by 12$ per customer.

The supply and demand equations are given by

- Demand Equation: p=140- 8aq
- Supply Equation: p=0.00005q
^{2 }+16bq+40

where q is the number of customers (in thousands per year); p is the price of dinner in dollar. a and b are coefficients to be chosen below.

Your task is to determine the impact of the 12$ price reduction on revenue.

Steps to complete the investigation

- Select 2 random numbers for a and b between 0.1 and 0.9 inclusive.
- Find the equilibrium price and quantity algebraically, without the price decrease.
- Update the demand question to include the 12$ price decrease.
- Use algebra to find the new equilibrium price and quantity.
- Use excel to graph on the same set of axes, the original supply and demand equation(from step 1) and the updated demand equation with the proposed price decrease(step 3).
- Use the results to complete the following summary table. Round answers to 2 decimal places , except for total revenue amounts which round to 0 decimal places.
- Summerise the findings in 300 words.a.In your conclusion:a.Discuss the effect of the price reduction on price, quantity and revenue.

b.Provide advice to the restaurant on whether to proceed with price decrease or not.

c. Note any assumptions you have made and any limitations of your findings.

**Marking Criteria: MAT10706 Quantitative Methods With Economics Assignment-Southern Cross University**

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