We are building a box. The price of the top and bottom mater side material is $3 per square inch. We also want the length o base and the enclosed volume to be 20 cubic inches. What dir
We are building a box. The price of the top and bottom mater side material is $3 per square inch. We also want the length o base and the enclosed volume to be 20 cubic inches. What dir
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Hi there, please help me with solving this problem please. Please clearly indicate all parts of answer(s). I would really appreciate if you could include all steps to solve the problem as well. Thank you very much!
Transcribed Image Text:3. We are building a box. The price of the top and bottom material is $15 per square inch and the cost of the
side material is $3 per square inch. We also want the length of the base to be 6 times the width of the
base and the enclosed volume to be 20 cubic inches. What dimensions will minimize the cost?
Quantity to optimize (with formula if possible):
Constraint:
Domain
in after getting a single-v
iable for
Transcribed Image Text:Guidelines for Optimization Problems
Read the problem carefully, identify the variables, and organize the given information with
a picture.
1.
Identify the objective function (the function to be optimized). Write it in terms of the
variables of the problem.
2.
3.
Identify the constraint. Write them in terms of the variables of the problem.
4.
Use the constraint to eliminate all but one independent variable of the objective function.
5.
With the objective function expressed in terms of a single variable, find the interval of
interest for that variable.
Use methods of calculus to find the absolute maximum or minimum value of the objective
function on the interval of interest. If necessary, check the endpoints.
6.
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