Portfolio Exercise 2

Linear Programming

SM Furniture Ltd manufacturestwo models of display cabinets, Basic(X) and Superior (Y). On a weekly basis the firm must produce at least 2 of each type, but not more than 5 Basic or more than 6 Superior. It takes 4 hours to produce the Basic model and 5 hours for the Superior model in a 40 hour working week. At least 12 workers are needed with 2 working on the Basic model and 3 on the Superior model at any one time.

Tasks

Part 1

1. Represent the above information as a system of inequalities.

2. Draw a graph of the system and indicate the feasible region clearly.

3. If the profit (P) on the Basic model is £800 and on the Superior model is £1000, write down the objective function in the form P = ax + by

4. Enter the relevant information into an Excel spreadsheet paying particular information to the layout of the sheet. It is important that this must be readable

5. Determine the number of each type that must be produced each week to make a maximum profit. Determine the maximum profit.

Part 2

1. Critically reflect on the use of Excel to provide a solution to this problem detailing any issues in either formulating the problem or determining the solution.

2. Critique the model which you have used in solving this using Excel. In particular comment on the setting used in setting up Solver.

3. Investigate the use of other software in solving linear programming problems in general.