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Simon Fraser University

Mathematics

MATH 157

Stephen Choi

Fall

Description

MATH 157 - D100A SSIGNMENT #5
Due date: Wednesday Feb 22, 2012
Instructor Questions accompanying paper Assignment # 5
Directions: Print double sided, write your solutions to both questions directly on this
page, place immediately after cover page and staple together!
Marks: An answer without a detailed solution process will be awarded zero marks!
Q1: Pulsar manufactures a series of 19-in. colour television sets. The quantity x of these sets
demanded each week is related to the wholesale unit price p by the equation
p = ▯0:006x + 180:
The weekly total cost incurred by Pulsar for producing x sets is
C(x) = 0:000002x ▯ 0:02x + 120x + 60;000
dollars.
a) Find the revenue function R and the proﬁt function P.
Solution: The Revenue function R(x) = p ▯ x = ▯0:006x + 180x. The proﬁt function
P(x) = R(x) ▯ C(x)
= (▯0:006x + 180x) ▯ (0:000002x ▯ 0:02x + 120x + 60;000)
= ▯0:000002x + 0:014x + 60x ▯ 60;000:
0 0
b) Find the marginal cost function C , the marginal revenue function R , and the marginal proﬁt
function P . 0
0 2
Solution: The marginal cost function C (x) = 0:000006x ▯0:04x+120. The marginal revenue function
0 0 2
R (x) = ▯0:012x + 180 and the marginal proﬁt function P (x) = ▯0:000006x + 0:028x + 60.
c) Compute C (2000);R (2000) and P (2000) and interpret your results.
Solution:
C (2000) = 0:000006(2000) ▯ 0:04(2000) + 120 = 64; R (2000) = ▯0:012(2000) + 180 = 156;
P (2000) = ▯0:000006(2000) + 0:028(2000) + 60 = 92:
To produce one more unit from 2000 to 2001, the extra cost is $64. To sell one more unit from 2000 to
2001, the extra revenue is $156 and the extra proﬁt is $92.

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