Year
slenue
Req) =
1932
1958
+1000 q
R 9)=-1000q
=74
1963
1968
COM
If the price in dollars of a stereo system is given by
1000
p(q)
+ 1000,
1000
²
q
where q represents the demand for the product, find the mar-
ginal revenue when the demand is 10.
54. Profit Suppose that for the situation in Exercise 53 the
cost in dollars of producing a stereo systems is given by
C(q) = 0.2q2 + 69 + 50. Find the marginal profit when the
demand is 10.
59. Marginal Product of Labor The output y of a manufacturing
y
process is a function of the size of the labor force n using the
function
1990
+1000
1971
1974
= 990
197
197
19
19
1
y = kVn.
The marginal product of labor, defined as dy/dn, measures the
rate that output increases with the size of the labor force, and is
a measure of labor productivity.
(a) Show that
(c) Using the
a cubic f
respond
the rate
and 200
(d) Discus
descri
part (
the y
(e) Exp
data
calc
ful
x
C(x) =
58. Money
1955-7
dy k
dn an
(b) How can you tell from your answer to part (a) that as the
size of the labor force increases, the marginal product of
labor gets smaller? This is a phenomenon known as the
law of diminishing returns, discussed more in the next
chapter.
56. Profit An analyst has found that a company's costs and rev-
enues in dollars for a product are given by
x2
C
and
R(x)
2x
2
5000'
respectively, where x is the number of items produced.
(a) Find the marginal cost function.
(b) Find the marginal revenue function.
(c) Using the fact that profit is the difference between revenue
and costs, find the marginal profit function.
(d) What value of x makes the marginal profit equal O?
(e) Find the profit when the marginal profit is 0.
(As we shall see in the next chapter, this process is used to find
marimum profit.)
A
wher
in bi
find
year
(a)
(C)
(e)
nad since
