Constraint Analysis

1. For the linear programming problem given in Question 3, the optimal solution is given by x=4 and y=0. Do a constraint analysis (that is, find the values of slack and surplus variables) for the optimal solution.

2. 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.

Formulate a linear programming model for the above situation by determining

(a) The decision variables.

(b) The objective function.

(c) All the constraints.

Note: Some of the questions above require drawing graphs. Here is a list of options for you to include a graph in your answer.

Draw the graph using MS Paint or CorelDraw or some other software. Copy the graph in a MS Word file and post the file on the course website in appropriate category.

OR

Draw the graph by hand on a paper, scan it and post it with your answer.

OR

Draw the graph by hand on a paper and describe the graph in words in your answer.