Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 13

For Problem:
a. How much labor and wood will be unused if the optimal numbers of chairs and tables are produced
b. Explain the effect on the optimal solution of changing the profit on a table from $100 to $500.
Problem
The Pinewood Furniture Company produces chairs and tables from two resources-labor and wood. The company has 80 hours of labor and 36 board-ft. of wood available each day. Demand for chairs is limited to 6 per day. Each chair requires 8 hours of labor and 2 board-ft. of wood, whereas a table requires 10 hours of labor and 6 board-ft. of wood. The profit derived from each chair is $400 and from each table, $100. The company wants to determine the number of chairs and tables to produce each day in order to maximize profit.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.