Question

The cost function for Acme Laundry is ​

C(q) = 20 + 30q + q2​
where q is tons of laundry cleaned. What q should the firm choose so as to maximize its profit if the market price is​ p?
The output level at which the​ firm's profit is maximized as a function of p is____.
If p = 100, then Acme Laundry should____produce units.

Answer 1

Step-by-step explanation:

The profit function will be:

π = Total revenue - Total cost

where,

Total revenue = price × quantity= pq

Total cost = 20 + 30q + q²

π = pq - (20 + 30q + q²)

π = pq - 20 - 30q - q²

Then we maximize profit with respect to q which will be:

dπ/dq = p - 30 - 2q

We then equate the profit function to 0.

p - 30 - 2q = 0

p - 2q = 30

2q = p - 30

q = (p - 30)/2

When p = 100, the number of units that should be produced will be:

= (p - 30)/2

= (100 - 30)/2

= 70/2

= 35 units