21-121 Calculus 1

Homework #9:

Exercises: Due Tuesday, November 5

Problem A: (In what follows, x^2 means "x squared".) Given the revenue and cost functions R = 50 x - 0.4 x^2 and C = 5x + 15, where x is the daily production (and sales), find the following when 40 units are produced daily and the rate of change of production is 10 units per day.

(i) The rate of change of revenue with respect to time (answer with the proper units)

(ii) The rate of change of cost with respect to time

(iii) The rate of change of profit with respect to time

Problem B: Repeat Problem A, given that 200 units are produced daily and the rate of change of production is 50 units per day.

Problem C: The demand function for a certain product is determined by the fact that the product of the price and the quantity demanded equals 8000. The product currently sells for $3.50 per unit. Suppose manufacturing costs are increasing over time at a rate of 15% and the company plans to increase the price p at this rate as well. Find the rate of change of demand over time.

Problem D: A company is increasing production at the rate of 25 units per day. The daily demand function is determined by the fact that the price (in dollars) is a linear function of q, the number of units produced (and sold). At a price of $70, the demand is 0, and 100 items will be demanded at a price of $60. Find the rate of change of revenue with respect to time (in days) when the daily production (and sales) is 20 items.

Section 3.11: 5-8, 11, 13, 14 (For problems 11, 13, and 14, just do the first part), 32, 38

Section 4.1: 3, 7, 21, 31, 32, 34, 37, 38, 50, 52, 57, 61