the business is failing should the company shut down its unprofitable operation.?

Question

The firm currently uses 70,000 workers to produce 300,000 units of output per day. The daily wage (per worker) is $100, and the price of the firm’s output is $30. The cost of other variable inputs is $500,000 per day. Although you don’t know the firm’s fixed cost, you know that it is high enough that the firm’s total costs exceed its total revenue.

Answer 1

Since total costs > total revenue you will contemplate shutting down your company in the long run, when you can change your fixed costs.
For the time during which your fixed costs are a given, however, you need to compare variable costs and revenue. If revenue exceeds variable costs, you keep operating because each day on which you keep operating, you will be making the extra amount of (daily revenue - daily costs) and hence limiting your loss to (fixed costs - that amount x number of days), whereas if you shut down, you would be incurring a loss in the amount of your total fixed costs, which would be greater.

In your case:

daily revenue = number of units produced per day * price per unit =
= 300,000 x $30 = $9,000,000

daily variable costs = number of workers * daily wage + daily cost of other variable inputs =
= 70,000 x $100 + $500,000 = $7,500,000

Daily revenue > daily variable costs
$9,000,000 > $7,500,000

Hence, by continuing to produce, each day during the period in which your fixed costs are fixed, you will be making an extra amount of
daily revenue - daily variable costs =
= $9,000,000 - $7,500,000 = $1,500,000
which you wouldn't be making if you shut down.
You can use this daily extra amount to at least reduce your losses.
Therefore you will stay in operation in the short run!!!

Answer 2

Yes, it should!