A furniture company makes tables and chairs. A table requires 40 board feet of w

Question

A furniture company makes tables and chairs. A table requires 40 board feet of wood and a chair requires 30 board feet of wood. Wood costs $1 per board foot and 40,000 board feet of wood are available. It takes 2 hours of skilled labor to make an unfinished table or an unfinished chair. Three more hours of labor will turn an unfinished table into a finished table; two more hours of skilled labor will turn an unfinished chair into a finished chair. There are 6000 hours of skilled labor available. (Assume that you do not need to pay for this labor.) The prices of output are given in the table below: Product Price Unfinished Table $70 Finished Table $140 Unfinished Chair $60 Finished Chair $110

1. Formulate a mathematical model for this problem. Be sure to state the decision variables, objective function and all the constraints.

Explanation / Answer

The relevant variables are the number of finished and unfinished tables

We can call them TF and TU ,

and the number of finished and unfinished chairs, CF and CU .

The revenue is (using the table): 70TU + 140TF + 60CU + 110CF , while the cost is

40TU + 40TF + 30CU + 30CF (because lumber costs $1 per board foot).

The constraints are:

1. 40TU + 40TF + 30CU + 30CF 40000.

2. 2TU + 5TF + 2CU + 4CF 6000.

The first constraint says that the amount of lumber used is no more than what is available.

The second constraint states that the amount of labor used is no more than what is available.

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