RCM2911 - Linear Optimisation Modelling Assignment

Assignment Task

Task

A real estate agent is fixing up a house for sale. She is deciding between painting, or new carpet, or both. Some analysis indicates that every square metre of new painting is worth $200 profit in sales, and every square metre of new carpet is worth $250 in sale profit. Painting costs $15 for each square metre, and takes half an hour; carpeting costs $25 for each square metre and takes a quarter of an hour. She has only $700 to spend, and only 14 hours available. And she wants to maximise her total sales profits.

1. Set up a resources table showing all information, costs, available resources, and sales profits.

2. Draw the feasible region, and determine the values of all vertices.

3. Solve the above problem using your diagram.

4. Also solve it using Excel Solver (include screenshots in your assignment, or upload the spreadsheet to the Dropbox), including the sensitivity analysis.

5. Determine the shadow price of each constraint by a graphical method and check the answers obtained by Excel.

6. Find the ranges of the profits for each of painting and carpeting, which does not affect the optimum value, by a graphical method.

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