Question 2 (2 points)

Question 2 options:

A box with a square base andopen top must have a volume of 55,296 cm³. We wish to find the dimensions of the box that minimize the amount of material used.

What the length of one side of the square base? Give the answer in centimeters.

Question 3 (8 points)

Question 3 options:

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola Y=6-X^2. What are the dimensions of such a rectangle with the greatest possible area? Approximate the width to 4 decimal places. Width =

Give the height as an integer or a fraction. Height =

A piece of cardboard measuring 8 inches by 13 inches is formed into an open-top box by cutting squares with side length X from each corner and folding up the sides. Find the value X for that will maximize the volume of the box. Approximate the answer to 3 decimal places. x =

Question 5 (8 points)

Question 5 options:

A cylinder shaped can needs to be constructed to hold 600 cubic centimeters of soup. The material for the sides of the can costs 0.03 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.07 cents per square centimeter. Find the dimensions for the can that will minimize production cost. To minimize the cost of the can:

Radius of the can approximated to 4 decimal places =

Height of the can approximated to 4 decimal places =

Minimum cost approximated to 2 decimal places =