Cost A manufacturer makes an open-top wooden crate having a volume of 18 cubic feet. Material costs are $0.20 per square foot for the base and $0.15 per square foot for the sides. Find the dimensions that minimize the cost of each crate. What is the minimum cost?
To calculate: The dimensions that minimize the cost of each crate and the minimum cost. If The volume of an open-top wooden crate is 18 cubic feet. the cost of material is $0.20 per square foot for the base and $0.15 per square foot for the side.
Given Information:
The provided figure is,
Formula used:
Consider a package (rectangular) of the following dimensions,
Then the volume is
Also, if there is a function
Step1:
Step2:
Calculation:
Let the length of the rectangular package be x, width be y and height be z.
Since, the volume of an open-top wooden crate is 18 cubic feet. so,
It can be written as
The cost of each crate is
Now find partial derivative of V with respect to y and z,
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