List some of the fixed and variable costs, which are likely to contribute to the costs shown in the table above.

Mathematics investigation relating to  business and calculations.

Viktor and Lily are equal partners in a Burnside business and have decided to explore opportunities to expand the products available to customers. They have a son, Bruce, who works part-time in the business. Bruce considers that there is a market for gift baskets containing fruit, nuts and confectionary, wine etc available in the shop, and decides to investigate the feasibility of setting up this venture as a sideline within the fruit and vegetable business.

Read the entire task and write an informative introduction that demonstrates your understanding of the situation to be investigated.

Mathematical Investigations

After some initial market research, Bruce decided to make 3 types of Gift Baskets that range in price from $70 to $100. These are shown below with the associated variable and fixed costs:

 

Type of basketSale PriceVariable CostsFixed Costs
Basic$70$38$9000
Regular$85$54$9000
Deluxe$100$62$9000

 

  1. List some of the fixed and variable costs, which are likely to contribute to the costs shown in the table above.
  2. Calculate the number of baskets required to break-even in each of the three scenarios listed above and calculate the revenue from these sales.
  3. Explain why these solutions do not give Bruce a useful indication of the number of baskets that he needs to sell in his business plan.

 

Bruce has now realised that he needs to focus on one specific type of basket. Select one type of basket above and using the variable and fixed costs given:

  1. State the sales revenue achieved when Bruce breaks even?
  2. Graphically display Bruce’s breakeven scenario, using appropriate technology.
  3. Discuss how realistic the breakeven number is for Bruce’s business.

Assuming that Bruce makes a profit in his first year of operating this business 

  1. Predict the number of  baskets sold and, from your graph, determine the profit made in this year.

In addition  to Bruce’s salary of $62,000 from working part-time in the fruit and vegetable business, he retains the profit from the sales of the gift baskets. 

  1. Calculate the tax payable including the Medicare levy and assuming he has private health cover.
  2. Find his net income.

Continued over page

 

  1. Using the same type of basket chosen previously, and initially assume the same number of sales in a year, use appropriate technology to investigate the effect of varying the sales price. You should consider:
    • The effect on the break-even number
    • Bruce’s net income
    • Representing your scenarios graphically
    • The effect of the change in sale price on the likely number of sales made.
    • The appropriateness of the sales price scenarios chosen Analysis/Discussion  Critically analyse your results, considering the appropriateness of each of the chosen sale price scenarios.

Conclusion

In concluding this task, justify your choice of the best scenario for Bruce, referring to the limitations of

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