MANUFACTURING
Response to the following problem:
Anderson & Blount (A&B) Woodworks makes tables and chairs from 30-inch wide mahogany sheets that it purchases by the linear foot. It can purchase whatever mahogany it desires for $ 1 0 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 nonnegativity 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. Solve for A&B's optimal weekly production schedule of tables and chairs. What is the optimal gross weekly profit? What is the optimal net weekly profit (gross weekly profit less the fixed labor, rent, insurance and utility costs)?
c. Determine and interpret the shadow prices for:
i. linear feet of mahogany
ii. cushions
iii. production hours