A wooden box without a top cover is to be made from layers of plywood (see...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
A wooden box without a top cover is to be made from layers of plywood (see figure below). The base is designed to be three-layers thick, the sides to be two-layers thick and the front and back to be one-layer thick. (a) (b) (c) Z y Front X Figure 04 Formulate a function giving the total area of plywood used that depends on the dimensions (x, y, z) of the box. (Only consider the area on one side of each layer of plywood.) (3 marks) If the volume of the box is required to be 3 m³, state the constrained optimization problem for the box to minimize its plywood usage and solve it for the desired dimensions. (15 marks) Without using any calculations, explain logically why the dimensions solved in Question 4(b) results in a constrained minimum (but not maximum) plywood usage. (6 marks) A wooden box without a top cover is to be made from layers of plywood (see figure below). The base is designed to be three-layers thick, the sides to be two-layers thick and the front and back to be one-layer thick. (a) (b) (c) Z y Front X Figure 04 Formulate a function giving the total area of plywood used that depends on the dimensions (x, y, z) of the box. (Only consider the area on one side of each layer of plywood.) (3 marks) If the volume of the box is required to be 3 m³, state the constrained optimization problem for the box to minimize its plywood usage and solve it for the desired dimensions. (15 marks) Without using any calculations, explain logically why the dimensions solved in Question 4(b) results in a constrained minimum (but not maximum) plywood usage. (6 marks)
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...
-
Start of Payroll Project 7-3a October 9, 20-- No. 1 The first payroll in October covered the two workweeks that ended on September 26 and October 3. This payroll transaction has been entered for you...
-
The first payroll in October covered the two workweeks that ended on September 26 and October 3. This payroll transaction has been entered for you in the payroll register, the employees' earnings...
-
State whether the following statement are True or False: Assets = Owners Equity is also a possible scenario.
-
Argonath Automotive, Inc., entered into the following transactions during the month of June: a. Purchased a total of eight new cars and trucks from Freddys Motors, Inc., for a total of $122,400,...
-
Macfarlane, Inc., recently issued new securities to finance a new TV show. The project cost $30 million and the company paid $1.9 million in flotation costs. In addition, the equity issued had a...
-
George Beemster, CPA, is examining the financial statements of the Louisville Sales Corporation, which recently installed an off-line electronic computer. The following comments have been extracted...
-
For each of the unrelated transactions described below, present the entry(ies) required to record each transaction. 1. Grand Corp. issued $20,000,000 par value 10% convertible bonds at 99. If the...
-
A car dealer acquires a used car for $14,000, with terms FOB shipping point. Compute total inventory costs assigned to the used car if additional costs include $250 for transportation-in. $300 for...
-
Hildreth Company uses a job order cost system. The following data summarize the operations related to production for April 2014, the first month of operations: a. Materials purchased on account, $...
-
5. [8] Write a bash script which takes any number of file names as command line arguments and prints whether each file is readable or not. Print a summary line as shown in the sample below. Sample...
-
Research www.hropenstandards.org. How many transactions or interfaces do the standards support? How many software vendors are involved with the organization?
-
Consumer product giant Proctor & Gamble (P&G) agreed to sell its portfolio of 43 beauty brands to beauty products maker Coty Inc. (Coty) for $12.5 billion on July 8, 2015. Included in the deal are...
-
What are the main functions of a database management system, and how is it different from a database?
-
Give examples of the types of actions that may be required by the parties to a proposed merger subject to an FTC consent decree.
-
Identify the initial and ongoing expenses related to the BCM program.
-
The ShowAllColors Procedure. Make a procedure to show all of the text color combinations. Use EAX for this. Choose a message to print (it can be anything: your name, your favourite food, etc.) You do...
-
In what ways does a well-designed enterprise search software vary from popular search engines (e.g., Bing, DuckDuckGo, and Google)?
-
Find the value of k such that the line kx - 3y = 10 (a) Is parallel to the line y = 2x + 4; (b) Is perpendicular to the line y = 2x + 4; (c) Is perpendicular to the line 2x + 3y = 6.
-
In Problems, find the indicated derivative. Assume in each case that x is restricted so that in is defined. (a) Dx In(x2 + 3x + ) (b) Dx In(3x3 + 2x) (c) Dx1n(x - 4)3
-
You suspect that the xy-data that you collect lie on either an exponential curve y = Abx or a power curve y = Cxd. To check, you plot ln y against x on one graph and ln y against ln x on another...
-
Which of the following are boiler mountings ? (a) Economiser (b) Fusible plug (c) Super heater (d) Injector
-
Which out of the following boiler is capable of generating superheated steam without additional accessories ? (a) Cochran (b) Lancashire (c) Locomotive (d) Cornish
-
The economiser of the boiler plant is used mainly to (a) increase steam capacity (b) reduce fuel consumption (c) increase steam pressure (d) increase life of the boiler
Study smarter with the SolutionInn App