menu
bartleby
search
close search
Hit Return to see all results

A company plans to manufacture a rectangular box with a square base, an open top, and a volume of 452 cm3. The cost of the material for the base is 0.4 cents per square centimeter, and the cost of the material for the sides is 0.6 cents per square centimeter. Determine the dimensions of the box that will minimize the cost of manufacturing it. What is the minimum cost?

Question
A company plans to manufacture a rectangular box with a square base, an open top, and a volume of 452 cm3. The cost of the material for the base is 0.4 cents per square centimeter, and the cost of the material for the sides is 0.6 cents per square centimeter. Determine the dimensions of the box that will minimize the cost of manufacturing it. What is the minimum cost?
 
check_circleAnswer
Step 1

The given box is in rectangular shape but has a square base with volume of the box as 452 cm3.

So consider the base and the sides of the rectangular box as x and y, respectively.

Thus, x2y = 452 cm3.

The cost for base is 0.4 cents and for sides is 0.6.

The surface area for the box can get the cost of the box.

Thus, c (x, y) = 0.4x2 + 0.6 (4xy).

Rewrite the volume as,

fullscreen
Step 2

Substitute y in c (x, y) as follows.

fullscreen
Step 3

Now find the value of x ...

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in

Math

Calculus

Differential Equations

Related Calculus Q&A

Find answers to questions asked by student like you

Show more Q&A add

Sorry about that. What wasn’t helpful?