a. Explanation Given: The perpendicular distance between Calverton to highway is 30 km, and capital city is 50 km down highway. The speed limit is r km/hour on the road and h km/hour on highway. Calculation: Given: T ( x ) has a critical point at x = 30 ( h r ) 2 − 1 . Let x be the distance from Q to the point P where the perpendicular joins the highway. Draw a diagram from the given data. The objective function is the time T ( x ) of the trip as a function of x . The time required to travel a distance d is t = d v . Use Pythagorean theorem. Find the road length. Length of road = 30 2 + x 2 Travel time from Calverton to Q is 30 2 + x 2 r The distance from Q to capital city = 50 − x Travel time from Q to capital city is 50 − x h The total number of hours for the trip is T ( x ) = 30 2 + x 2 r + 50 − x h For the critical point. T ' ( x ) = 0 x r 30 2 + x 2 − 1 h = 0 ⇒ x r 30 2 + x 2 = 1 h ⇒ h x = r 30 2 + x 2 ⇒ ( h x ) 2 = ( r 30 2 + x 2 ) 2 ⇒ h 2 x 2 = r 2 ( 30 2 + x 2 ) ⇒ h 2 x 2 = 30 2 ⋅ r 2 + r 2 x 2 ⇒ h 2 x 2 − r< b. To determine Describe the travel -time function has a given critical point.

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.6, Problem 19E

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Describe the travel -time function has a given critical point.

To determine

Describe the travel -time function has a given critical point.

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Chapter 4.6, Problem 18E

Chapter 4.6, Problem 20E

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Describe the travel -time function has a given critical point.

Solution Summary: The author describes the travel -time function with a given critical point. The objective function is the time T(x) of the trip.

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Describe the travel -time function has a given critical point.

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