A designer is making a rectangular prism box with maximum volume, with the sum of its length, width, and height 8 in. The length must be 2 times the width. What should each dimension be? Round to the nearest tenth of an inch if necessary. A. width: 2 in. length: 4 in. height: 2 in. B. width: 1.8 in. length: 3.6 in. height: 2.6 in. C. width: 3.6 in. length: 1.8 in. height: 2.6 in. D. width: 4 in. length: 2 in. height: 2 in.

B. Width: 1.8 in. Length: 3.6 in. Height: 2.6 in.

Step-by-step explanation:

Let x represent width of the rectangle and y represent height of the prism.

We have been given that the length must be 2 times the width. So length of the prism would be .

We are also told that the sum of its length, width, and height 8 in. We can represent this information in an equation as:

We know that volume of rectangular prism is product of length, width and height.

Upon substituting the values of length, width and height, we will get:

Upon substituting equation (1) in volume formula, we will get:

Now, we will take the derivative of volume function using power rule as:

Now, we will equate derivative with zero and solve for x as:

Since width cannot be 0, therefore, the width of prism would be 1.8 inches.

Length of the prism would be .

Therefore, the length of prism would be 3.6 inches.

Upon substituting in equation (1), we will get:

Therefore, the height of prism would be 2.6 inches and option B is the correct choice.