The Internet Economy

1.The cost of producing q items is given by

C(q) = 15q^(2/3) + 100q + 10,000. Find where this cost function is increasing and where it is decreasing. Sketch the graph of C(q).

2. If a company sells q items per day, then the price of each item is given by

P(q) = 10 – q/10

Find the range where the revenue function R(q) =qp(q) is increasing and where it is decreasing.

3. The cost of producing q items is given by C(q) = 100 +50q + 0.2q³. Find dC/dq and d² C/dq^2 at q = 0, 5, 50, and 75.

4. The postage for shipping an item weighing q ounces is modeled by

P(q) = Q(Q^2 +1)^(0.5)

Find the dP/dq and d²P/dq² when q = 1, 10 and 20.

5. If the marginal profit is given by P^’(q) = 2q ^–1/2, find a model for the profit P(q).

6. Suppose the daily profit (in dollars) from manufacturing q items is modeled by P(q) = -0.01q² + 5q – 400, where 0£ q £ 300. Find the number of items q that results in maximum profits.

7.  Suppose the cost (in dollars) of manufacturing q items is modeled by C(q) = 400+ 10q +0.01q². Find the value of q that minimizes the average cost function.