A manufacturer estimates that when x

units of a particular commodity are produced, the total cost will be:

C(x)=18x2+3x+98

dollars,

and furthermore that all x

units will be sold when the price is:

p(x)=13(75−x)

dollars per unit.

a. Find the marginal cost,

b. Find the marginal revenue,

c. Estimate the marginal profit from producing the 37
-th unit. What is the actual cost of producing the 37-th unit?