Explanation Given information: 1. Two production units, A and B are situated 1000 miles apart along a straight ,/p> 2. Per unit production cost at location A is $ 20 less than at location B . 3. Route of delivery of computers is along a straight line and delivery cost is 25 cents per unit per mile. Formula used: 1) Standard form of a hyperbola whose center is origin is x 2 a 2 − y 2 b 2 = 1 2) Distance Formula: Distance between two points A ( x 1 , y 1 ) and B ( x 2 , y 2 ) is A B = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 Calculation: In below pictorial representation point A ( − 150 , 0 ) and B ( 150 , 0 ) is location of two assembly unit. And point C ( x , y ) is the location of customer where computers need to be delivered. Calculating BC and AC using distance formula B C = ( x − 500 ) 2 + ( y − 0 ) 2 = ( x − 500 ) 2 + y 2 miles A C = ( x + 500 ) 2 + ( y − 0 ) 2 = ( x + 500 ) 2 + y 2 miles Route of delivery of computers is along a straight line and delivery cost is 25 cents per unit per mile. Total delivery cost for route B C will be, 0.25 × ( x − 500 ) 2 + y 2 dollars. Total delivery cost for route A C will be, 0.25 × ( x + 500 ) 2 + y 2 dollars. Per unit production cost at location A is $ 20 less than at location B . And total cost needs to be same from both locations. i.e. 20 + 0.25 × ( x + 500 ) 2 + y 2 = 0.25 × ( x − 500 ) 2 + y 2 ⇒ 80 + ( x + 500 ) 2 + y 2 = ( x − 500 ) 2 + y 2 { Dividing both sides by 0

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Author: Ratti

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Chapter 8, Problem 78RE

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The equation of the curve at any point of which the computers can be supplied from either location at the same cost.

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Chapter 8 Solutions

Precalculus: A Unit Circle Approach

Ch. 8.2 - Prob. 1E Ch. 8.2 - Prob. 2E Ch. 8.2 - Prob. 3E Ch. 8.2 - Prob. 4E Ch. 8.2 - Prob. 5E Ch. 8.2 - Prob. 6E Ch. 8.2 - Prob. 7E Ch. 8.2 - Prob. 8E Ch. 8.2 - Prob. 9E Ch. 8.2 - Prob. 10E

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The equation of the curve at any point of which the computers can be supplied from either location at the same cost.

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The equation of the curve at any point of which the computers can be supplied from either location at the same cost.

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