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Lecture

# 157IQsol5.pdf

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School
Simon Fraser University
Department
Mathematics
Course
MATH 157
Professor
Stephen Choi
Semester
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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