A certain item sells for $30. If the cost of producing this item is given by C = .05s^3 + 100, find the marginal profit when x = 10.

Answer 1

There is no x in the production cost formula!

C = .05s^3 + 100

I assume you mean "when s=10".

Cost of 10 units
= 0.05(10)³ + 100
=$150

Cost of 11 units
= 0.05(11)³ + 100
= $166.55

So what is the marginal cost, marginal profit?

Using calculus, the marginal cost would be:
C'(s)
= 0.15s²
So
C'(10)
=0.15*10²
=$15

The discrepancy will diminish as the production quantity get larger.