3. Anderson & Blount (A&B) Woodworks (3 points)

(Adapted from Lawrence and Pasternack, Chapter 2 Problem 5)

Anderson & Blount (A&B) Woodworks makes tables and chairs from 30-inch wide mahogany sheets that it purchases the linear foot. It can purchase whatever mahogany it desires for $10 per linear foot up to 2250 linear feet per week. Each table requires 9 linear feet and each chair 3 linear feet (including waste). Each chair also utilizes a soft cushion. Up to 500 cushions can be purchased each week for $25 each. Other required hardware (supports, braces, nuts, bolts, etc.) averages $45 for each table and $25 for each chair. A&B sells the tables to retailers for $300 each and each chair for $150 each.

The 10 craftsmen employed by A&B are salaried workers. To produce a table requires 1 hour of a craftsmen's time, whereas each chair requires only 36 minutes. Each craftsman averages 37.5 productive work-hours per week. Company policy mandates that the ratio of chairs to tables must be between 4 to 1 and 6 to 1.

a. Develop a linear programming model for A&B. The objective function should maximize its weekly profit (revenue less the variable costs of wood, cushions and other materials). Express the feasible region by the non-negativity constraints and a set of five functional constraints (wood and cushion availability, the minimum and maximum chair to table ratios, and the maximum weekly production time).

Hints on ratio constraints: if you define # of chairs as C, # of tables as T, then the minimum ratio will be expressed as C/T >= 4, which is equivalent to C >= 4T (by multiplying both side by T) then to C - 4T >= 0 (by moving 4T from right to left).

b. Apply graphical analysis to draw each constraint and identify the resulting feasible region and the optimal solution with the line of same profit method.

c. Use solver add-in to solve the problem.