Question

# 1. Consider the following optimization problem. Find two positive numbers x and y whose sum is...

1. Consider the following optimization problem. Find two positive numbers x and y whose sum is 50 and whose product is maximal. Which of the following is the objective function?

A. xy=50

B. f(x,y)=xy

C. x+y=50

D. f(x,y)=x+y

2. Consider the same optimization problem. Find two positive numbers x and y whose sum is 50 and whose product is maximal. Which of the following is the constraint equation?

A. xy=50

B. f(x,y)=xy

C. x+y=50

D. f(x,y)=x+y

3. Consider the same optimization problem. Find two positive numbers x and y whose sum is 50 and whose product is maximal. Solve the problem. What are the optimal values for x and y?

A. x=1, y=49

B. x=20, y=30

C. x=25, y=25

D. x=50, y=50

4. For y=x^2+.5x^3 on the interval -2 <= x <= 1, which of the following is the global maximum?

A. x= 1

B. x= -2

C. x= 0

D. x= .5

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