A company plans to manufacture a rectangular bin with a square base, an open top, and a volume of 800 cm3. The cost of the material for the base is 0.1 cents per square centimeter, and the cost of the material for the sides is 0.5 cents per square centimeter. Determine the dimensions of the bin that will minimize the cost of manufacturing it. What is the minimum cost?

Question
Asked Nov 27, 2019
6 views

A company plans to manufacture a rectangular bin with a square base, an open top, and a volume of 800 cm3. The cost of the material for the base is 0.1 cents per square centimeter, and the cost of the material for the sides is 0.5 cents per square centimeter. Determine the dimensions of the bin that will minimize the cost of manufacturing it. What is the minimum cost?

check_circle

Expert Answer

Step 1

According to the given information:

Let length of the rectangular bin be ‘x’ cm

Breadth of rectangular bin = ‘x’ cm

Height of rectangular bin = ‘y’ cm

Volume = 800 cm3

So,

help_outline

Image Transcriptionclose

lengthx breadth x height 800 xy volume 800 У y = х?

fullscreen
Step 2

Cost of material for base = 0.1 cents per square centimeters

Cost of material for sides = 0.5 cents per square centimeters

So, the total cost for rectangular bin TC is:

help_outline

Image Transcriptionclose

TC 0.1(x)+0.5(4xsy) 800 TC (x) 0.1(x)+0.5(4) (x)| х 1600 TC(x)-0.1x2 х

fullscreen
Step 3

Now, to minimize the cost use sec...

help_outline

Image Transcriptionclose

1600 TC'(x0.2x TC'(x) 0 1600 = 0 0.2x- 1600 1600 0.2x 0.2 x= 8000 x = 20

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Derivative