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  3. 2 dean runsandnbspthe creamy barandnbspwhich specialises in artisan ice cream...

Question: 2 dean runsandnbspthe creamy barandnbspwhich specialises in artisan ice cream...

Question details

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 amount 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:

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

  2. (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?

  3. (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:

  1. (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?

  2. (b)  What is the maximum profit per market day if Dean paid $1.2 per litre 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?

  3. (c)  DuetothepopularityoftheChocolateAlmondFudgeflavour,Deanishopingtoincreasethepriceto $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?

  4. (d)  Inpreparationforthescorchingheatinsummer,Deanwouldliketopurchaseanextra10litresofmilk 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.

  1. 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).

    Here are a few points to consider while working through this assignment question:

    1. The first step is always to work out the mathematical set up for the problem. This means identifying decision variables, formulating the objective function and then formulating constraints. At this stage, we are not trying to solve the problem or work out interactions among constraints. We simply list all conditions that must be satisfied.

      When you complete Task 1, you should have two decision variables, the objective function written in terms of those decision variables, and five constraints, also written in terms of decision variables (some using both decision variables, others just one of them).

    2. The second step is to find a solution. Task 2 tells you specifically to use Excel Solver to find this solution. The key here is to translate all mathematical expressions from Task 1 into Excel format. Instructions for doing so can be found under Topic 5 in the Excel booklet, as well as in the Linear Programming supplement. In addition, the Lecture notes page in this website gives you access to Excel spreadsheets used to generate Excel output shown in lecture slides for Week 5. It may be worthwhile examining them before attempting Task 2.

    1. The final step is interpreting the solution that has been found, which is Task 3.

    2. The report in Task 4 is a summary of the results from linear programming and sensitivity analysis in Tasks 2 and 3.

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