Related Rates Calculus problem DUE TOMORROW!! HELP PLEASE!!!?

Question

Boise, Idaho is about 300 miles inland from the nearest point on the Pacific Coast; San Diego is about 1000 miles south of the point down the coast. Assuming the coast is a straight line going north south, C is the point along the coast directly west of Boise. It costs 2 cents/mile to transport a ton of potatoes by truck and 1 cent/mile to transport a ton of potatoes by ship. The Idaho Potato company wants to find the point P on the Pacific Coast to which it should truck it's potatoes before loading them aboard a cargo ship in order to minimize the cost of transporting them from Boise to San Diego. A) Set up the function which the Idaho potato company must minimize. B) find the position of P which minimizes cost.

Answer 1

let x be # of miles south of C...

0.02 * sqrt(90k + x^2) + 0.01 * ( 1000 - x) = C = cost
dC/dx = 0.01 ( 2x/sqrt(90k + x^2) - 1) = 0
1 = 2x/sqrt(90k + x^2)
sqrt(90k + x^2) = 2x
(90k + x^2) = 4x^2
90k = 3 x^2
x = 100 √3

Answer 2

let the point p be x miles from c
distance to be covered by ship=(x^2 + 300^2)^(1/2)=k
distance to be covered by truck=1000-x
cost of the transporting/ton of potato=2k+1000-x
so we have to minimize
f(x)=2(x^2 + 300^2)^(1/2)+1000-x
f'(x)=2x/(x^2 + 300^2)^(1/2)+(-1)
for minimum f'(x)=0
we get x=+-173.02
we neglect -ve answer as it gives maximum
therfore answer is p=173.02 miles south of c
thanks
hey feanor don't u know 90k/3=30k

Answer 3

if the distance of the person from the light is x, the height of shadow is given by h/6 = 20/x h = 120 / x dh/dt = -120/x^2 * dx/dt when x = 8, dx/dt = 2.5 dh/dt = -120/64 * 2.5 = -250/64 ~= -4 ft/sec