Reference no: EM132330215

Question 1 - Impact of changing price upon revenue and profit

A factory worker makes small electronic toys. One of the more popular items made in the factory is a remote control drone. Each drone requires an outer metal housing and electronic parts which are placed inside the casing. The factory worker uses three types of outer housing - silver, chromium and titanium. Drones are then distributed to toyshops for sale. Drones are assembled and sold as follows;

Regardless of the type of metal housing used to make each drone, there are fixed production costs of $250.

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

Steps to complete to undertake the investigation

1. Find the total cost and total revenue functions for each type of drone 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 drone within the price ranges in the table above.

2. Confirm any points of intersection between the cost and revenue function lines using algebra.

3. Profit will also differ for each drone. Find the profit functions and the break-even point for each drone.

4. Summarise your findings in 200 words. In your conclusion:

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 drone (for example, which drone 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 price discount on revenue

A restaurant by a beach is renowned for its menu featuring fresh seafood caught locally. One year, local fishermen catch a larger than normal amount of seafood. To clear excess seafood, the restaurant must reduce the average price of its dinners. The restaurant manager decides to reduce the dinner price by $15 per customer.

Your task is to determine the consequences of the $15 price reduction. The supply and demand equations are given by

Demand Equation: p = 150 - 10aq

Supply Equation: p = 0.00001q² + 2bq + 20
where q is the number of customers (in hundreds per year) ; p is the price of a dinner in dollars.
a and b are coefficients to be chosen below.

Steps to complete to undertake the investigation

1. 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 $15 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

7. Summarise your findings in 300 words. In your conclusion:
a) Discuss the effect of the surcharge on price, quantity and revenue
b) Provide a recommendation to the restaurant on whether to introduce the price decrease or not
c) Note any assumptions you have made and any limitations of your findings.