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

Here we need to choose the variables for the number of finished and unnished tables,

lets denote

finished tables = XF

and

XU = number of unfinished tables

, and the number of finished and unfinished chairs,

YF and YU respectively

. Theobjective function could be found using the data for costs gives in the problem

        Z1 = 70XU+ 140XF+ 60YU + 110YF   {this objective funcition is for the revenue}

now we'll have to give the objective function for the cost as well

we are given that wood costs $1 per board foot

Z2 = 40XU+ 40XF+ 30YU + 30YF        {this objective funcition is for the cost}

the constraints

The constraints are:

40XU + 40XF + 30YU + 30YF <= 40000 (this is for the quantity of wood used)

2XU+ 5XF + 2YU + 4YF <= 6000      (this is for the skilled hours or the amount of labour used)

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