The Pinewood Furniture Company produces chairs and tables from two resources—labor and wood.
business
Description
Chapter 2: problem 5, 9, 29, 35
5. 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 to
maximize profit. a. Formulate a linear programming model for this problem. b.
Solve this model by using graphical analysis.
9. Solve the following linear programming
model graphically: maximize Z = 3x1 + 6x2 subject to 3x1 + 2x2 ... 18 x1 + x2 Ú
5 x1 ... 4
x1, x2 Ú 0
29. Solve the following linear programming
model graphically: minimize Z = 8x1 + 2x2 subject to 2x1 - 6x2 ... 12 5x1 + 4x2
Ú 40 x1 + 2x2 Ú 12 x2 ... 6
x1, x2 Ú 0
35. Assume that the objective function in
Problem 34 has been changed from Z = 30x1 + 70x2 to Z = 90x1 + 70x2. Determine
the slope of each objective function, and discuss what effect these slopes have
on the optimal solution.
