Probem47+Meredith+Jana



RT = 6 RF = 2 TF = 4√2 EF = x TE = 4√2 - x So RE = √(2² + x²) = √(4+x²)

If it costs $800,000 to build through the river and $400,000 to build over land Underwater cost = (800,000)(√(4+x²)) + (400,000)(4√2 - x) = (400,000)[2√(4+x²) + (4√2 - x)] --> i think this is the objective function I took the derivative of the equation I found above, and I got C' = (400,000)[(2x)/(√(4+x²)) - 1], which when set equal to zero gives you x = 1.1547 If you plug that in you get that the point is 4.8 km east of the refinery Also, the image that was posted on this page just disappeared when i put in my diagram thing ... so I apologize to whoever posted that. i really have no idea how to retrieve it.

Hey meredith, it's eric g, try this: so for above ground I'm getting x-6 because the only traveling you'll be doing on land is AFTER you've already crossed the river and that is subtracted from the 6km. then for underwater its jussttt when youre traversing the river so I believe it's just √(4+x²) I'm getting the equation to be

C(x) = 400,000(6-x) + 800000(squrt (x²+1)) derive that and see if you don't get the right answer...