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Solve each problem as requested and demonstrate that you have found the optimum value.

1. The height (in feet) of a flare shot upward from the ground is by the function:

s(t)=6+1121-16², where t is the time in seconds. What is the maximum height that the

flare rises to?

12

2. In 1998, the projected US Social Security Fund assets (S) in 10 ¹2 dollars (trillion dollars)

was given by the function: S(t)=-0.00074³ +0.02² +0.8 where t is the number of

years after 2000. In what year will the fund be maximized and how much will that

maximum be?

assignment/n3. A rectangular microprocessor chip is designed to have 25 mm of area. What should the

dimensions of the microprocessor be to minimize the perimeter?

4. Jack wants to build three dog kennels on the side of his house. If he has 80 feet of

fencing, what are the overall dimensions of the kennels that maximize the area?

Wall

y

X

y

y

Fig: 1

Fig: 2