What can you conclude from this number line? #1

If y=2x-8, what is the minimum value of the product xy? #8

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. #10

Find two real numbers whose difference is 500 and whose product is a maximum. #19

Find two real numbers whose difference is 500 and whose product is a minimum. #20

A rectangle has an area of 81 cm^2.

What is the maximum perimeter possible? #23

Farmer Jo has 32 square feet of land in which to make an enclosure for bunnies, chicks, and penguins. (see picture)

Choose the equation that represents this information. #2

same question, now solve it and answer the question:

Farmer Jo has 32 square feet of land in which to make an enclosure for bunnies, chicks, and penguins.  There will be fencing put around the entire enclosure and in the middle (as pictured) to create 3 sections, what dimensions should the overall enclosure be to use the least amount of fence? #3

A rectangle is bounded by the x-axis and the parabola  $$y=12-x^2$$ .  What length and width should the rectangle have so that its area is a maximum?  

Given the constraint equation above and the optimization equation  $$A=2xy$$  , choose the DERIVATIVE of the merged (combined) equation. #6

What is the process of optimization in calculus? #15

A farmer wants to construct a rectangular pigpen using 400 ft of fencing. The pen will be built next to an existing stone wall, so only three sides of fencing need to be constructed to enclose the pen. What dimensions should the farmer use to construct the pen with the largest possible area? #7

Pick the correct interpretation from the given number line for V', the derivative of V. #9

You want to make a box to contain dirt and your pet earthworm. Using a 7 in by 10 in a rectangle of cardboard, you cut congruent squares from the corners and fold up the sides.

Choose the equation would you use to do Calculus to find the maximum volume of dirt (including worms) the box can hold. #13

A closed rectangular shipping box with a square base is to be made from 120 square inches of cardboard. What dimensions should the box be for maximum volume?

Choose the constraint and optimization equations that represent the problem. #5

The volume of a cylindrical tin can with a top and a bottom is to be 16π cubic inches. If a minimum amount of tin is to be used to construct the can, what must be the height, in inches, of the can? #16