Math 103. Homework 7. Due 4/3/02

1. [61, p. 221] Find an equation of the tangent line to the graph of the function

f(x)=x   _____ Ö2x2+7

at the point (3,15).

2. [13, p. 237] The Pulsar corporation manufactures certain model of 19-inch color TV sets. The quantity x of these sets demanded each week is related to the wholesale unit price p by the equation

p=-0.006 x +180

The weekly total cost incurred by Pulsar for producing x sets is

C(x) = 0.000002 x3 -0.02 x2 +120 x+60,000

dollars.

(a) Find the revenue function R and the profit function P.
(b) Find the marginal cost function C¢, the marginal revenue function R¢ and the marginal profit function P¢.
(c) Compute C¢(1000), R¢(1000) and P¢(1000) and interpret your results.

3. [15, p. 237] Find the average cost function

C

associated with the total cost function of the previous problem.

(a) Find the marginal average cost function




C   ¢


(b) Compute




C   ¢(5000)       and        C   ¢(10,000)

and interpret your results.

4. The management of the Titan Tire Company has determined that the quantity demanded x of their Super Titan tires per week is related to the unit price by the equation

p = 144-x2

where p is measured in dollars and x in units of a thousand.

(a) Compute the elasticity of the demand when p= 63 and 108.
(b) Interpret the results obtained in part (a).
(c) For what values of p is the demand unitary?

5. [30, p. 238] The quantity demanded per week x (in units of a hundred) of the Mikado miniature camera is related to the unit price p (in dollars) by the demand equation

5p = 400-x2        (0 £ p £ 80)

(a) Is the demand elastic or inelastic when p=40? When p=60?
(b) If the unit price is lowered slightly from $60, will the revenue increase or decrease?
(c) If the unit price is increased slightly from $40, will the revenue increase or decrease?