Question

If a company's cost function for a product is

C(q) = 2280 + 3.8q + 0.004q²

and the revenue function is

R(q) = 12.2q − 0.002q²,

find the production level that maximizes profit.
................................. units

Answer 1

Given cost function:

C(q)=2280+3.8q+0.004q2

Revenue function: R(q)=12.2q-0.002q2

Profit function P(q)=R(q)-C(q)-----(1)

So, P(q)=(12.2q-0.002q2)-(2280+3.8q+0.004q2)

P(q)=12.2q-0.002q2-2280-3.8q-0.004q2

P(q)=8.4q-0.006q2-2280----(2)

Production level (q) which maximises profit can be found by differentiating P(q) with respect to q and equating the function to zero.

So, from (2)

[Since: , and

]

So the production level that maximises profit is

70 units.