In the first case (Total Fixed Cost equal one million:
Total variable cost equal $ 4.4M ($ 4M for wages (fifty thousand workers time eighty dollars per worker) plus four hundred thousand other variable inputs. Average variable cost equal twenty two dollars (Total variable cost of $4.4M plus Total fixed cost one million divided by Two hundred thousand units) worker productivity equal four ( Two hundred thousand units divided by fifty thousand workers Profit/loss equal four hundred thousand loss (Total revenue of two hundred thousand units times twenty five dollars price equal 5.4M (Total cost can be calculated either by taking the average total cost times two hundred thousand units or by taking the total variable cost plus the total fixed cost)
In the second case (Total Fixed Cost equal $3M):
Total variable cost not changed at $4.4M average total cost not changed at twenty two dollars average total cost not changed equal thirty seven dollars 9 $4.4M total fixed cost divided by two hundred thousand units) worker profit/loss equal $2.4M loss (total revenue remains at $5M; total cost equal $7.4M) If I recall a shutdown rule is if a firm can cover total variable cost at some level of production in the short-run, it could keep operating. Personally, I believe a fixed cost is very irrelevant in a short-run because it stacks cost. Moreover, the firm receives twenty-five dollars with variable cost of twenty two dollars with variable cost it would not shut down immediately in neither cases.
Now for the break-even number of workers:
In the first case, it would be: four hundred thousand loss divided by eighty dollars per worker, or five thousand; layoff five thousand workers leaving a workforce of forty five thousand.
In the second case, it would be: two million and four hundred thousand loss divided by eighty dollars per worker, or thirty thousand; lay off thirty thousand workers leaving a workforce of twenty thousand.
All of this assumes that the production remains at two hundred thousand units per day; this is unlikely, but you have to assume this with the information given. This changes the worker productivity to: four point four (as opposed to four) in the first case (two hundred thousand unit times the new workforce of forty-five thousand. Ten (as opposed to four) in the second case (two hundred thousand unit times the new workforce of Twenty thousand)
The first case is more likely to happen; it is asking remaining employees to increase production by eleven percent (four point four over four then times one hundred) this level of increases happen all the time during a recession. The second case is not likely to happen; it is asking remaining employees to increase production