Calculus Optimization Problems Day 1

Which of the following should be maximized?

• Profit

• Cost

• Time

• Plant performance

Which of the following should be minimized?

• Profit

• Cost

• Time

• Staff Utilization

Find two real numbers whose sum is 400 and whose product is a maximum.

• 200 and 200

• 300 and 100

• 250and 150

• -200 and -200

• Cannot be determined

Find two real numbers whose sum is 400 and whose product is a minimum.

• 200 and 200

• 300 and 100

• 150 and 250

• -200 and -200

• Cannot be determined

Find two real numbers whose difference is 500 and whose product is a maximum.

• 250 and 250

• 400 and -100

• 150and -350

• 250 and -250

• Cannot be determined

Find two real numbers whose difference is 500 and whose product is a minimum.

• 250 and 250

• 300 and -200

• 150and -350

• 250 and -250

• Cannot be determined

Find two positive numbers such that the sum of the first number and five times the second number is 40, and their product is maximum.

• 25 and 3

• 15 and 5

• 20 and 4

• 35 and 1

• Cannot be determined

There are two positive numbers, such that the sum of the first number and five times the second number is 40.

What is the maximum value of the product of the two numbers that is possible?

(a follow up from the last question)

• 100

• 75

• 80

• 120

Find two positive numbers such that the sum of two times the first number and eight times the second number is 400; and their product is maximum.

• 150 and 12.5

• 120 and 20

• 100 and 25

• 80 and 30

• Cannot be determined

There are two positive numbers such that the sum of two times the first number and eight times the second number is 400.

What is the maximum value of the product of the two numbers that is possible?

Type in your answer below.

(a)