Linear programming problem

[fobster]

I got a LP problem that I'm stuck on.

A furniture factory makes tables and chairs. It takes 2 hours to assemble a table and 30 minutes to assemble a chair. Assembly is carried out by four people on the basis of one eight-hour shift per day. Customers buy at four chairs with each table which means that the factory has to make at most four times as many chairs as tables. The selling price is €135 per table and €50 per chair.

Formulate this as a linear programming problem to determine the daily production of tables and chairs which would maximise the total daily revenue to the factory and solve the problem using the simplex method.

My progress:

X1 = Amount of tables produced
X2 = Amount of chairs produced

Max Z = 135X1+50X2

Subject to:
120X1+30X2 ≤ 1920
4X1 ≥ X2
X1, X2 ≥ 0

Standard form:

Max Z = 135X1+50X2

Subject to:
4X1+X2+S1 = 64
4X1-X2-S2 = 0
X1, X2, S1, S2 ≥ 0

Are my constraints correct?



Thanks for your time.

[Rassis]

Yes, they are correct and the result must be 8 tables and 32 chairs selling for €2,680.

Try to reach these same conclusions yourself using the simplex method.

[Glaysher]

Actually there is a minor error

4X1+X2+S1 = 1920

should be either

120X1+30X2+S1 = 1920

or

4X1+X2+S1 = 64

[fobster]

Actually there is a minor error

4X1+X2+S1 = 1920

should be either

120X1+30X2+S1 = 1920

or

4X1+X2+S1 = 64

Just a typo by me.

[Glaysher]

Then you are fine