Explanation Given: The demand fora manufacturer’s product is increasing at the rate of2%/year The current demand is 5,000 units/year Price remains fixed at $400/unit Calculation: Consider a manufacturer's product whose demand is increasing exponentially at the rate of 2% per year. Current demand is 5.000 units per year, so demand after t years will be, D ( t ) = 5000 e 0.02 t ......(1) Price remains fixed at $ 400 per unit. So, revenue function will be, R ′ t = 400 × D ( t ) = 400 × 5000 e 0.02 t = 2 , 000 , 000 e 0.02 t Use the formula for the cumulative change for a quantity Q ( x ) , "If Q ′ ( x ) is the rate of change of the quantity Q ( x ) , then cumulative change for Q ( x ) over time-period [a, b] will be obtained by the definite Integral. Q ( b ) − Q ( a ) = ∫ a b Q ′ ( x ) d x ′ ′ ......(2) For 2 years, t = 12 × 2 = 24 Substitute, the values in the above expression, R ′ ( t ) = 2 , 000 , 000 e 0

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 6.6, Problem 39PS

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To find: the total future revenue received by the manufacturer

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Chapter 6.6, Problem 38PS

Chapter 6.6, Problem 40PS

Chapter 6 Solutions

Calculus

Ch. 6.1 - Prob. 1PS Ch. 6.1 - Prob. 2PS Ch. 6.1 - Prob. 3PS Ch. 6.1 - Prob. 4PS Ch. 6.1 - Prob. 5PS Ch. 6.1 - Prob. 6PS Ch. 6.1 - Prob. 7PS Ch. 6.1 - Prob. 8PS Ch. 6.1 - Prob. 9PS Ch. 6.1 - Prob. 10PS

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the total future revenue received by the manufacturer

Solution Summary: The author explains the formula for the cumulative change for a quantity Q(x).

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To find: the total future revenue received by the manufacturer

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Chapter 6 Solutions