HWoct 23, 7ogName: Cisselle WashingtonOptimization problemsDate:Period:A man launches his boat froma point on the bank of a straight, rectangular lake.The man can row at the rate of 6 mi/hr and can run at 8 mi/hr. He wants to reach apoint 8 miles downstream and on the other bank (point B). The river is 3 mileswide. Assume the speed of the water is negligible. He could row directly across thelake (point D) and run down the bank or he could row directly to the point B acrossthe lake or he could row to a point somewhere in the middle (C) and run the rest ofthe way. How can he reach point B in the least time?Find the area of the largest rectangle that can be inscribed in an equilateral triangle

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Step 1

Let he rows to point C which is in the middle of B and D. Then he runs to B.

Let C is x miles away from D. If x=0 then C=D , if x=8 then C=B.

So if we find x then we can find which will be the best way for him.

Step 2

CD=x, BC=8-x.

We need to find AC= ? We will use Pythagorean theorem.

AC= sqrt(x^2+9)

Step 3

Time = Distance/ Speed

For rowing Distance = sqrt(x^2+9) miles and speed= 6 mi/hr

For runnin...

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