Crossposted at Operations Research SE
The mechanical workshop can produce $600$ units of part #1 or $1200$ units of part #2 per shift. The production capacity of the thermal workshop, where these parts are sent for heat treatment on the same day, allows for processing $1200$ units of part #1 or $800$ units of part #2 per shift. The prices of both parts are the same. It is necessary to determine the daily production program of parts that maximizes the company's output, given the additional condition that both workshops work one shift.
So, in the end we obtain a mathematical model of the given problem in the form of a linear programming problem, both the objective function and the constraint functions should be linear. Which can also be solved using simplex method.
Example can be found here.
All I want is right determination of function and its limitation (I believe it could also be called "mathematical model") to the problem itself as in example, so I could start solving it by myself. Sorry for misunderstanding.
If the “or” is exclusive, in that we can’t have mixed production, then the model would be:
$$\max\quad z = c_1 x_1 + c_2 x_2$$ Subject to: $$x_1 \le 600 y_1$$ $$x_2 \le 1200 (1-y_1)$$ $$\frac{x_1}{1200} + \frac{x_2}{800} \le 1$$ $$x_1, x_2 \ge 0, y_1\in\{0,1\}$$
If it is not, in that we are able to have mixed production: $$\max\quad z = c_1 x_1 + c_2 x_2$$ Subject to: $$\frac{x_1}{600} + \frac{x_2}{1200} \le 1$$ $$\frac{x_1}{1200} + \frac{x_2}{800} \le 1$$ $$x_1, x_2 \ge 0$$
Finding the optimal solution of either case is left to you.