Section 4.6 page 299 #11 How much of each type of A portion of the shoreline of

Question

Section 4.6 page 299 #11

How much of each type of A portion of the shoreline of an island is in the shape of the curve y = 2 A hut is located at point C, as shown below. Supplies are delivered by boat to the shoreline. It costs $10 per mile to hire someone to transport the supplies from the shore to the hut. At what point (x, y) on the shoreline should the supplies be delivered to minimize overland transportation costs? How much does the overland transportation cost? How much of each type of A portion of the shoreline of an island is in the shape of the curve y = 2 A hut is located at point C, as shown below. Supplies are delivered by boat to the shoreline. It costs $10 per mile to hire someone to transport the supplies from the shore to the hut. At what point (x, y) on the shoreline should the supplies be delivered to minimize overland transportation costs? How much does the overland transportation cost?

Explanation / Answer

coat will be less when distance is minimum
hut locates at (100,0)
let (x,y) be nearest point
distance
s=sqrt((x-100)^2 +y^2)
=((x-100)^2 +4x)
=(x^2-196x+10000)
ds/dx=0
==>2x-196=0
==>x=98
==>y=298=142

point on parabola is (98,142)

cost=s*10=(2^2 +196) *10

=200 *10

=1002

=141.4$

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