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157IQsol10.pdf

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Department
Mathematics
Course
MATH 157
Professor
Stephen Choi
Semester
Fall

Description
MATH 157 - D100A SSIGNMENT #10 Due date: Wednesday April 04, 2012 Instructor Questions accompanying paper Assignment # 10 Solution 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: The weekly demand for the Pulsar 25-inch colour console television is given by the demand equation p = ▯0:05x + 600 (0 ▯ x ▯ 12;000) where p denotes the wholesale unit price in dollars and x denotes the quantity demanded. The weekly total cost function associated with manufacturing these sets is given by 3 2 C(x) = 0:000002x ▯ 0:03x + 400x + 80;000 where C(x) denotes the total cost incurred in producing x sets. Find the level of production that will yield a maximum profits for the manufacturer. Solution: Since 2 R(x) = p ▯ x = ▯0:05x + 600x: so MR = ▯0:1x + 600: Also 2 MC = 0:000006x ▯ 0:06x + 400: Set MR=MC, we get 0:000006x ▯ 0:06x + 400 = ▯0:1x + 600 or 0:000006x + 0:04x ▯ 200 = 0 ▯0:04+0:08 Hence x = 2▯0:00006
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