Why does this approach fail?

Question

We have the following statement (translated from Spanish to English):

A company manufactures skirts, blouses and pants. To do this, use a machine for each type of clothing. The machine for skirts costs €200/month, the machine for blouses costs €150/month and the machine for pants costs € 120/month.

The hours and fabric consumed by each type of clothing are in this table:

Each month 150 hours and 160 square meters of fabric are available.

The unit profit and cost per type of clothing is shown in this table:

We want to maximize profit, and I propose the following model:

This results in the following optimal table if we use the simplex method:

If we subtract the cost of the machines from the € 300 profit, we have € -50 left.

Why are there losses? I imagine my initial model is wrong, but I don't know why.

Answer 1

Ignoring the fabric limitations to simplify things we can see that skirts and blouses have a profit of 2€/hour (pants are less). This tells us that at best with only 150 hours available every month your profit is indeed caped at 300€. This is why you have losses - the machines are too expensive.
Two additional remarks:
Are you sure that the time limit of 150 hours is a limit on the total time of all three machines and the cost of each machine doesn't depend on its usage?
Since the per hour profit of skirts and blouses is the same you could simply produce 75 blouses (150h and 140$m^2$ of fabric). This gives you 300€ - 150€ = 150€ profit since you are not using two of the three machines.

Answer 2

The function to be maximized would be the following:

With the following restrictions

So we have the relaxed problem (in Spanish, that's what we call problems without integer variables):

The simplex table is as follows

The optimal simplex table is as follows

So the optimal value is 150 €

We have to add the following restrictions to the original approach

These restrictions guarantee an upper bound in case clothing is manufactured and, if clothing is not manufactured, it will be zero.

The upper bound for each type of clothing is calculated by dividing the total hours available during the month by the hours used to manufacture said clothing.

It would also have been worth calculating the upper bound from the available fabric, but I´m not going to prove it.

Also, we have to add y1,y2,y3 to the objective function with its corresponding technological coefficients as we can see at the beginning of this answer.