Help with volume -calculus 3

Question

A parcel delivery service requires that the dimensions of a rectangular box be such that the length plus twice the width plus twice the height be no more than 108 inches (L+2W+2H <= 108). What is the volume of the largest volume box the company will delivery? 

Answer 1

1. V = LWH

 

2. L = 108 -2W - 2H

 

3. Substitute (2) in (1)

 

4. Take ∂V/∂W AND ∂V/∂H set each equal to zero.

 

5. You should see that W=H.

 

6. Substitute into (3)

 

7. This will give V as a function of one variable

 

8. Take the derivative and set it equal to zero to solve for W.

 

9. That will then give you L and H.

 

 

Any questions comment back. (I believe you should get L=36, H=18, W=18)