requestbook
54

Step-by-step Answer
PAGE: 213SET: ExercisesPROBLEM: 54
Please look in your text book for this problem Statement

(a).

Volume of the closed box with a square base is cub. in

The volume and square area  of a box with square base length  and height .

Therefore, .

(b).

(1). Draw the coordinate plane.

(2). Graph the function .

Graph :

 

 

.

(c).

The minimum amount of cardboard used corresponds to the graph of with the smallest

-coordinate.

Graph :  

 

Observe the garph :

The graph has minimum point at .

Therefore, the minimum amount of cardboard used is and this occurs when .

(d).

Consider .

Differentiate the above function with respect to .

Equate to zero.

The dimensions of the box that minimize the surface area are .

(e).

UPS is interested in designing a box that minimizes the surface area because to minimize the cost of materials used for the construction.

(a).

.

(b).

Graph  of :

 

(c).

Minimum amount of cardboard used is  and this occurs when .

(d).

.

(e).

To minimize the cost of materials used for the construction.



TESTIMONIALS

"I want to tell you that our students did well on the math exam and showed a marked improvement that, in my estimation, reflected the professional development the faculty received from you. THANK YOU!!!"

June Barnett

"Your site is amazing! It helped me get through Algebra."

Charles

"My daughter uses it to supplement her Algebra 1 school work. She finds it very helpful."

Dan Pease

QUESTIONS? LET US HELP.
Simply chose a support option

My status

JOIN US ON:     
mathskey.com is not affiliated with any Publisher, Book cover, Title, Author names appear for reference only