Problem 2: Furniture making (25 marks)

Westport Furniture produces a line of furniture that replicates some classic designs from the late 1800s. Currently the company makes a rocking chair, formal dining tables and armoires. A production plan for the next week is being formulated. The company has no problem selling everything in this line that it makes.

Furniture goes through two production stages cutting/assembly and finishing. The wood used is a fine grade of cherry and its supply is limited. The table below gives the resources required for each item and the availability of each resource over the next week.

Over the next week the company has available 3600 minutes of cutting/assembly time, 2000 minutes of finishing time and 4000 Kg of wood.

1) Formulatetheproblemasalinearprogram.Clearlydefineyourdecisionvariablesasafirst step.

2) Enter the problem in Excel and use Solver to get the optimal solution. Include both the answer report and sensitivity report with your submission (well labeled).

3) What is the optimal profit represented by the objective function and what is the optimal production plan?

4) What are the binding constraints?

5) The company owner has promised his mother a rocking chair. What will the new profit be

if tis promise is honoured?

6) The selling price of tables has suddenly decreased by $110 dollars (nothing else has changed). What will be the effect on the optimal solution?

7) An additional 100 minutes of finishing time can be purchased for an amount that is $2 above what it currently costs? Should the extra time be bought and if so, what will be the effect upon the optimal solution?

8) Afireinthewoodwarehousehasreducedtheamountofwoodby500Kg.Whatwillbe the effect upon the optimal solution?

\begin{tabular}{|l|c|c|c|} \hline & Rocking Chair & Dining table & Armoire \\ \hline Cutting/Assembly (minutes) & 100 & 180 & 120 \\ \hline Finishing (minutes) & 60 & 80 & 80 \\ \hline Wood (Kg) & 30 & 180 & 120 \\ \hline Unit profit & $240 & $720 & $600 \\ \hline \end{tabular}