2.  

Packaging

By cutting away identical squares from each corner of arectangular 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 yieldthe maximum volume. (Round your answers to two decimal places ifnecessary.)

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

3.

Minimizing Packaging Costs

A rectangular box is to have a square base and a volume of 36ft³. 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 boxthat can be constructed at minimum cost. (Refer to the figurebelow.)

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

x= ?ft   y=? ft

4.

Book Design

A book designer has decided that the pages of a book should have1 in. margins at the top and bottom and one half in in. margins onthe sides. She further stipulated that each page should have anarea of 98 in.² (see the accompanying figure). Determinethe page dimensions that will result in the maximum printed area onthe page.

x= ?in y= ?in

7.

Racetrack Design

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

r=? ft   l=? ft

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

? ft²

Please answer eachquestion. Thank you