Question 176820This question is from textbook college algebra/ blitzer
: The firm currently uses 50,000 workers to produce 200,000 units of output per day. The daily wage (per worker) is $80, and the price of the firm’s output is $25. The cost of other variable inputs is $400,000 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.
So far I have come up with the TVC being $800,000. Quantiy sold is 500,000, but i am still having trouble any suggestions. All help is appreciated.
This question is from textbook college algebra/ blitzer
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! cost per worker = $80.00 per day.
50,000 workers * $80.00 per day = $4,000,000 per day.
price per unit = $25.00.
200,000 units per day * $25.00 = $5,000,000 per day.
cost of other variable inputs is $400,000 per day.
Profit = Revenue minus Cost
cost = fixed cost plus variable cost.
variable cost = $4,000,000 per day plus $400,000 per day = $4,400,000 per day.
revenue = $5,000,000 per day.
your profit formula is:
let p = profit.
let r = revenue
let x = fixed cost
let v = variable cost
p = r - (x + v)
r = $5,000,000
x = x
v = $4,400,000
p = $5,000,000 - (x+$4,400,000)
removing parentheses gets:
p = $5,000,000 - x - $4,400,000
combining like terms gets:
p = $600,000 - x
since cost exceeds profit, this means that profit has to be less than or equal to $0.00
this means that:
p <= $0.00
since p = $600,000 - x, this means that:
$600,000 - x <= $0.00
subtract $600,000 from both sides of the equation and it becomes:
-x <= $600,000
multiply both sides of the equation by (-1) and it becomes:
x >= $600,000
since multiplying both sides of an inequality by (-1) reverses the inequality.
your answer:
fixed cost has to be greater than or equal to $600,000.
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