Question

2.  

Packaging

By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 16 in. long and 6 in. wide, find the dimensions (in inches) of the box that will yield the maximum volume. (Round your answers to two decimal places if necessary.)

smallest value=? in ?in largest value =?in

3.

Minimizing Packaging Costs

A rectangular box is to have a square base and a volume of 36 ft³. If the material for the base costs $0.24/ft², the material for the sides costs $0.15/ft², and the material for the top costs $0.16/ft², determine the dimensions (in ft) of the box that can be constructed at minimum cost. (Refer to the figure below.)

A closed rectangular box has a length of x, a width of x, and a height of y.

x= ?ft   y=? ft

4.

Book Design

A book designer has decided that the pages of a book should have 1 in. margins at the top and bottom and one half in in. margins on the sides. She further stipulated that each page should have an area of 98 in.² (see the accompanying figure). Determine the page dimensions that will result in the maximum printed area on the page.

x= ?in y= ?in

7.

Racetrack Design

The accompanying figure depicts a racetrack with ends that are semicircular in shape. The length of the track is 1056 ft (1/5 mi). Find l and r such that the area of the rectangular region of the racetrack is as large as possible. (Round your answers to the nearest foot.)

r=? ft   l=? ft

What is the area enclosed by the track in this case? (Round your answer to the nearest square foot.)

? ft²

Please answer each question. Thank you

Answer 1