I am unsure about how to solve the following optimization question. **Problem Statement:**Find the dimensions of the least expensive rectangular box which is three times as long as it is wide and which holds 100 cubic centimeters of water. The material for the bottom costs $0.07/cm², the sides cost $0.05/cm² and the top costs $0.02/cm².---**Explanation:**This problem involves finding the optimal dimensions for a rectangular box given specific conditions on its proportions and a target volume. Here's the breakdown:1. **Proportions and Volume:** - The box's length (L) is three times its width (W). - The volume of the box is 100 cubic centimeters.2. **Cost considerations:** - Bottom cost: $0.07 per square centimeter. - Side cost: $0.05 per square centimeter. - Top cost: $0.02 per square centimeter.**Objective:**Minimize the fabrication cost while maintaining the required volume and proportions.

Answered: Image /qna-images/answer/f475241d-5a87-4df4-baca-8d765221bca0.jpg

4. Find the dimensions of the least expensive rectangular box which is three times as long as it is wide and which holds 100 cubic centimeters of water. The material for the bottom costs $0.07/cm², the sides cost $0.05/cm? and the top costs $0.02/cm².

4. Find the dimensions of the least expensive rectangular box which is three times as long as it is wide and which holds 100 cubic centimeters of water. The material for the bottom costs $0.07/cm², the sides cost $0.05/cm? and the top costs $0.02/cm².

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...

See similar textbooks

Related questions

Q: Question 13 Write the number that corresponds to the correct answer. What is the treatment in this…

A: Treatment is the independent variables manipulated by the researcher. The dependent variable is…

Q: 5) Maximizing Revenue You are the marketing manager for LTCC Ski Area, from the previous experience,…

A: The question mentions that the manager can sell 3000 lift tickets when the price is set at $40. Now,…

Q: Valencia Products make automobile radar detectors and assembles two models: LaserStop and…

A: Maximize profits.t.and

Q: Annie's Apartments is looking to maximize their revenue this year. Annie noticed that when rent was…

Q: 3. Mang Gustin observed that when he uses x units of fertilizer, he is able to yield 1 m(x) = − −x¹…

A: To find the maximum yield we need to use the concept of maxima and minima. First we need to find the…

Q: Given right AABC with AC = 8 and BC = 10:A rectangle is constructed in AABC as shown in the diagram.…

A: In the figure shown as - ABC is the triangle with,AC = 8 cmBC = 10 cmLet,Length of the rectangle =…

Q: There is a maximum of 6,000 hours of labor available per month and 300 ping-pong balls (x1) or 200…

Q: Solve the following application problem, pertaining to maximizing area. You must show your work ……

A: Given:Let x be a widthLength=200-2xArea of rectangle =length×breadth

Q: In an optimization problem, how many variables should eventually occur in the function we are trying…

Q: The Minimum point of y = 8x+4 (x-2)²

A: Use a graphing utility to plot the function. Use the utility to determine the minimum point.

Q: Solve the optimization problem. Minimize F = 37x² + 37y2 with xy² = 16. F =

Q: In an optimization problem, how many variables should eventually occur in the function we are trying…

A: We have find the how many variables eventually occur in the function in an optimization problem.

Q: 15(b). The demand function fora manufacturer's product is p =7.2 – 0.0045q where p is the price per…

Q: 5. Crunchy Coco Hunks cereal comes in a rectangular box that must be exactly 4 inches deep. If the…

Q: Kara's Custom Tees experienced fixed costs of $500 and variable costs of $5 a shirt. Write an…

Q: A rectangular storage container with an open top is to have a volume of 32 cubic meters. The length…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Explain the effects of imposing a constraint in an optimization problem. Give at least one economic…

A: Effect of imposing a constraint in an optimization problem with one economic example.

Q: 5. A two-pen corral is to be built. The outline of the corral forms two identical adjoining…

Q: A car rental agency rents 300 cars per day at a rate of $55 per day. For each $1 increase in the…

A: A car rental agency rents 300 cars per day at a rate of $55 per day. For each $1 increase in the per…

Question

I am unsure about how to solve the following optimization question.

**Problem Statement:**

Find the dimensions of the least expensive rectangular box which is three times as long as it is wide and which holds 100 cubic centimeters of water. The material for the bottom costs $0.07/cm², the sides cost $0.05/cm² and the top costs $0.02/cm².

---

**Explanation:**

This problem involves finding the optimal dimensions for a rectangular box given specific conditions on its proportions and a target volume. Here's the breakdown:

1. **Proportions and Volume:**
- The box's length (L) is three times its width (W).
- The volume of the box is 100 cubic centimeters.

2. **Cost considerations:**
- Bottom cost: $0.07 per square centimeter.
- Side cost: $0.05 per square centimeter.
- Top cost: $0.02 per square centimeter.

**Objective:**

Minimize the fabrication cost while maintaining the required volume and proportions.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Please answer it clearly
How do you determine if an LP problem has alternative optimal solution
This question is in the course of Optimization Theory. I need the answer ASAP and thank you SO MUCH in advance.
need comprehensive and correct answers.This question is about optimization.
Answer each of these optimization questions. Identify what is to be optimized, what is the constraint, and show all necessary work in solving these questions.
2. The speed of sound, d, in feet per second is given by the function 3. Со- d(T) = (T + 896.16), where T is the air temperature in degrees Celsius. Part A: What is a feasible domain for the function d(T)? Par Part B: What is a feasible range for the function d(T)? Part C: Sketch the graph of the model above. (Hint: Use 100's for the input.) Par d T Part D: Predict the speed of sound in air at 25°C. Part E: Based on the model above, at what temperature would the speed of sound in air be 5 ft/s? MATH NATION Practice Book - Section 8: Expressions and Equations
Just do part b,c and d
Wire of length 12 m is divided into two pieces and the pieces are bent into a square and a circle. How should this be done in order to minimize the sum of their areas? Only set up. No need for the solution to the problem. Set up the objective function using the following notation: Let x represent the length of the piece of wire that is to be bent into a square.
Please do A and B
Q4: Please show exact detailed steps for each problem
Use the revenue function R(x) : 3) x² + 200x with domain [0, 6000] that was discussed above. (a) If the goal is to maximize Revenue, what price should the company charge for the hoverboards, and how many hoverboards should be produced? Illustrate your solution with a graph of the Revenue function. Student #17 (Presentation CP3): (See MyLab Homework H64 problem [1] and study [Example 1] in the Notes from the Video for Homework H64.) You will be continuing the example started by Student #16, using the revenue function R(x) : = x² + 200x with domain [0, 6000] that was discussed above. 30 Suppose also that the Cost function is C(x) = 60,000 + 20x (b) Find the Profit function, P(x). (c) If the goal is to maximize Profit, what price should the company charge for the hoverboards, and how many hoverboards should be produced? Illustrate your solution with a graph of the Profit function.
Answer Please, thanks!