Science and Maths - Assignment Help

Science and Maths  Assignment Help

Assignment Task:

1. Motion Music is doing a financial feasibility analysis for a new album. Recordings and production are estimated at $65,000. The printing of CDs is fixed at S5000 for set up plus $3 per CD. The artist's royalty is 4% per CD of the publisher's price to music stores. Advertising and promotion costs are
budgeted at $9,000.

(a) If the price to music stores is set at $21, how many CDs must be sold to break even? Find the break-even point algebraically and by using an EXCEL graph. Attach the printout or copy your EXCEL graph into your assignment submission. EXCEL Instructions: Create a column called Number of CDs and in that column enter values
from O to 5,000 in increments of 500. Then create two more columns, one for Total Cost and another for Total Revenue. Enter appropriate formulae in EXCEL to obtain the total cost and total revenue corresponding to each value in the Number of CDs column. Highlight the resulting three sets Of numbers and go to the Insert tab (or Chart menu) to obtain an appropriate diagram. Make sure that your graph has been labeled appropriately (i.e. title, axis labels, legend). Refer to Topic 3 in the EXCEL Supplement for further instructions on entering formulae and graphing in EXCEL.

(b) The marketing department is forecasting sales of 5,000 CDs at the price of $21. Based on your graph from part (a), will there be a net profit or net loss from the project at this volume of sales? How do you know? Calculate this net profit or loss amount. (Assume no tax costs.)

(c) If the artist requires an increase in royalty to 7%, how does this impact Motion Music? Assuming the fixed costs and the selling price remains as in (a), explain in a short paragraph (3- 4 sentences) whether the number of CDs required to break-even will increase or decrease. QQ for this question however you may quote the break-
even formula to aid your explanation.

(d) The marketing department is also forecasting that if the price is reduced by 5% then unit sales will be 10% higher. Should Motion Music continue with the original price in (a) or this reduced price? Show calculations that support your recommendation. Assume initial fixed and variable cost estimates.

2. Dean runs The Creamy Bar which specialises in artisan ice cream sold at a local farmer's market. Prevailing prices in the local market are $8 for a take-home tub of Classic Vanilla and $15 for a tub of Chocolate Almond Fudge.

The local dairy farmer delivers 48 litres Of milk every Friday in preparation for market day. Classic Vanilla will need 0.5 litres per tub and Chocolate Almond Fudge requires 3 times as much. Both flavours require 500g of sugar to enhance the taste. There is a total of 20kg of sugar available per market day. For the signature velvety mouthfeel, Dean adds 0.5 litres Of heavy cream to Classic Vanilla and double the arnount for Chocolate Almond Fudge. He ordered 50 litres Of heavy cream from the supplier.

Task 1
Construct a mathematical model for this problem. In doing so, consider the following:

(a) What are the decision variables for this problem?

(b) Using decision variables identified in part (a), formulate the Objective function for this problem. Is the quantity of interest to be maximised or minimised?
(c) What constraints are relevant to this problem? Using the decision variables from part (a), formulate those constraints.

Task 2
Use Excel Solver to Obtain a solution to the mathematical problem from Task 1. Your submission should include:
• your Excel spreadsheet the Sensitivity Report
• the Answer Report

Task 3
Use your Excel output to answer the following questions:

(a) Describe the linear programming solution to the Dean Of The Creamy Bar in terms Of:

• The optimum number Of take-home tubs Of Classic Vanilla and Chocolate Almond Fudge to prepare each market day.
• The maximum revenue per market day.
• Whether all the milk purchased will be fully utilised.
• Whether all the sugar allocated will be fully utilised.
• Whether all the heavy cream ordered will be fully used.
Which Of the Solver reports helps you answer these questions?

(b) What is the maximum profit per market day if Dean paid $1.2 per liter for milk and cream and $45 for sugar? Note that Dean also draws a $100 salary per market day.
Which Solver report allows you to answer this question?

(c) Due to the popularity Of the Chocolate Almond Fudge flavor, Dean is hoping to increase the price to $20 per take-home tub. Would the solution obtained in Task 2 still be optimal? Which of the EXCEL reports helps you answer this question? Justify your answer carefully. How would the solution and The Creamy Bars' revenue change, if at all?

(d) In preparation for the scorching heat in summer, Dean would like to purchase an extra 10 liters of milk to increase ice cream production. Would the solution obtained in Task 2 still be optimal? Which of the EXCEL reports helps you answer this question? Justify your answer carefully. How would the solution
and The Creamy Bars' revenue change, if at all? Attach the new Answer Report ONLY, for the scenario in which Dean purchases 58 litres of milk,
verifying your calculated maximum revenue per market day.

Task 4
Write a report outlining the solution and discussing your findings from Task 3 (at most two pages, double-spaced, at least 2cm margins, 12pt Times New Roman font or equivalent).

3. A simple random sample Of 220 university students were asked what pasta they usually order and with which sauce. The preferences of these respondents are summarised below:

(a) Use Excel to Obtain a 100% stacked column chart for the data from the table. What does your chart suggest between the relationship between Pasta and Sauce?
EXCEL Instructions: Refer to Topic 6 in the Excel Booklet for instructions on how to obtain 100% stacked column chart.

(b) Use the contingency table to calculate the following probabilities; include an appropriate probability Statement for each case:

1.  What is the probability that a respondent prefers Spaghetti?
2. What is the probability that a respondent prefers Gnocchi and Carbonara sauce?
3. What is the probability that a respondent prefers Ravioli or Pesto sauce? Suppose the preferred sauce is Bolognese. What then is the probability the pasta ordered is Spaghetti?
4. Suppose that the preferred Pasta is Ravioli. What then is the probability the sauce ordered is Carbonara?

(c) Are the events Spaghetti and Sauce statistically independent or dependent? How do you know? Show all calculations that support your answer.

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