# 2. The cost of producing x units of a certain commodity is given by P�x � 1000 �

0

x

MC�sds,

where P is in dollars and M�x is marginal cost in dollars per unit.

A. Suppose the marginal cost at a production level of 500 units is $10 per unit, and the cost

of producing 500 units is $12, 000 (that is, M�500 � 10 and P�500 � 12000).

Use a tangent line approximation to estimate the cost of producing only 497 units.

B. Suppose the production schedule is such that the company produces five units each day.

That is, the number of units produced is x � 5t, where t is in days, and t � 0 corresponds to

the beginning of production. Write an equation for the cost of production P as a function of

time t.

C. Use your equation for P�t from part B to find dP

dt . Be sure to indicate units and describe

what dP

dt represents, practically speaking.