UAB MBA 662 Anderson & Blount (A&B) Woodworks makes tables
Question # 00379391
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Updated on: 09/06/2016 12:55 AM Due on: 09/06/2016
MBA662 HW1
Dr. Nuo Xu
(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. Their wages of $800 each per week as well
as the $5000 per week in rent, insurance and utility costs are all considered fixed costs. 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 gross
weekly profit (gross 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).
b. Apply graphical analysis to draw (to scale) each constraint and indentify the resulting feasible
region.
Dr. Nuo Xu
(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. Their wages of $800 each per week as well
as the $5000 per week in rent, insurance and utility costs are all considered fixed costs. 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 gross
weekly profit (gross 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).
b. Apply graphical analysis to draw (to scale) each constraint and indentify the resulting feasible
region.
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Solution: UAB MBA 662 Anderson & Blount (A&B) Woodworks makes tables