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 be solved using simplex method.
Simply speaking, I need the problem above to be described in linear equation with constraints.
Example (not related to the problem above):