Question

A docking facility 4 miles off shore stores large amounts of oil. It is to be connected by a pipe to a refinery onshore.. 8 miles down the shore line from facility as shown in the figure. If underwater pipe cost $3,000 per mile and land-based pipe cost $2,000 per mile, what solution of piping would minimize the cost of connection? Show equations and determine solution with calculator.

Docking Facility mi Shore line Refinery B 8 mu

Answer 1

let AB = x miles PB² = PA²+ AB? PB² - 4² + x² Umiles C PB = 16+ x2 A B and BC = (8-2) miles C(x) = 3000 / 16+x² + (8-2) +2000 8 miles C'(x) = 3000 X (2x) + (0-1)x2000 2/16 tx² c'(x) = 30oon - 2000 16 tu? c'(x) = 0 Do. 3000X - 2000 V 16tuz 3r - V 16t42 9x2 = 4 16+ 22

q x² = 64+ 4 x ² 5x²= 64 x= √64 x- & x = 3.58 miles

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