Answer:
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