The Flair Furniture company makes tables and chairs. Each table requires 4 hours of carpentry labour and 2 hours of painting labour to be made. Each chair requires 3 hours of carpentry labour and 1 hour of painting labour to be made. There are 240 carpentry hours and 100 painting labour hours available. The marketing department believes they can sell all the tables but, based on current stock, require no more than 60 chairs. Each table sold generates $7 profit contribution and each chair sold yields $5 profit contribution. Create a linear programming model for the case above. In your model ensure that you have an objective function, constraints and a non-negativity condition. Using the model created in part 1, determine the best possible mix of tables and chairs to generate the maximum profit for the firm.
LEARNING ACTIVITY 7.1
Read the following scenario and answer the questions below.
The Flair Furniture company makes tables and chairs. Each table requires 4 hours of carpentry labour and 2 hours of painting labour to be made. Each chair requires 3 hours of carpentry labour and 1 hour of painting labour to be made. There are 240 carpentry hours and 100 painting labour hours available.
The marketing department believes they can sell all the tables but, based on current stock, require no more than 60 chairs. Each table sold generates $7 profit contribution and each chair sold yields $5 profit contribution.
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Create a linear programming model for the case above. In your model ensure that you have an objective function, constraints and a non-negativity condition.
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Using the model created in part 1, determine the best possible mix of tables and chairs to generate the maximum profit for the firm.
LEARNING ACTIVITY 7.2
Answer the question below.
Based on the basic/fundamental theorem of linear programming, differentiate between a basic feasible solution and a basic feasible optimal solution. Use mathematical examples where appropriate.
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