State the problem in linear programming terms and solve it using the simplex method.

Question

A furniture manufacturing company plans to make two products chairs and tables from its available resources, which consist of 400 board feet of mahogany timber and 450 man hours of labor. Making a chair requires 5 board feet and 10 man hours and yields a profit of sh. 45/=, while each table uses 20 board feet and 15 man hours and has a profit of sh 80/=. As the production manager you are required to determine how many chairs and tables the company can make keeping within the available resource constraints, so that it maximizes the profit. Let X 1 and X 2 be the production of chairs and tables respectively.

Answer 1

Here is a video response with matrices (the simplex tableau); I hope it helps. I apologize for the length of the video; simplex method problems take a while! Please let me know if I can clarify anything for you.

Answer 2

Tashia

Board feet used : 5 x1 + 20 x2 ≤ 400, simplifying to x1 + 4 x2 ≤ 100

Man hours used : 10 x1 + 15 x2 ≤ 450, simplifying to 2 x1 + 3 x2 ≤ 90

Let's assume x1 corresponds to x, and x2 corresponds to y

Then you need to draw the region bounded by x=0. y=0. x + 4y ≤ 100, 2x + 3y ≤ 90

This shows our resource constraints

The region has 4 vertices , the origin (0,0), a point on the x axis, on the y axis, and where the two lines x+4y = 100. and 2x+3y = 90 intersect.

The profit will be 45 x + 80 y, so you need to calculate this at each of these 4 vertices.

The vertex giving the highest profit will be your solution.

Mike