You need to make a closed box with total volume 1500 cubic inches, but you want to spend as little money as possible. Material for the front and back of the box costs 90 dollars per square inch. Material for the top and bottom of the box costs 100 dollars per square inch. Material for the remaining two sides of the box costs 80 dollars per square inch. a) What should the dimensions of the box be? Please enter the dimensions as a list (in any order). Round each entry to the nearest hundredth. length, width, height =| 11.49,10.22,12.77 %3D b) What is the lowest possible cost for this box? minimum cost = | 70777.98

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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This is a calculus 3 problem. Please explain each step clearly, no cursive writing.

You need to make a closed box with a total volume of 1500 cubic inches, but you want to spend as little money as possible.

- Material for the front and back of the box costs 90 dollars per square inch.
- Material for the top and bottom of the box costs 100 dollars per square inch.
- Material for the remaining two sides of the box costs 80 dollars per square inch.

a) What should the dimensions of the box be? Please enter the dimensions as a list (in any order). Round each entry to the nearest hundredth.

Length, width, height = **11.49, 10.22, 12.77**

b) What is the lowest possible cost for this box?

Minimum cost = **70777.98** dollars

In this problem, we are tasked with minimizing the cost of materials required to construct a box of a specified volume by determining its optimal dimensions.
Transcribed Image Text:You need to make a closed box with a total volume of 1500 cubic inches, but you want to spend as little money as possible. - Material for the front and back of the box costs 90 dollars per square inch. - Material for the top and bottom of the box costs 100 dollars per square inch. - Material for the remaining two sides of the box costs 80 dollars per square inch. a) What should the dimensions of the box be? Please enter the dimensions as a list (in any order). Round each entry to the nearest hundredth. Length, width, height = **11.49, 10.22, 12.77** b) What is the lowest possible cost for this box? Minimum cost = **70777.98** dollars In this problem, we are tasked with minimizing the cost of materials required to construct a box of a specified volume by determining its optimal dimensions.
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