MTH61204 Engineering Mathematics I Assignment 1 (individual) @ 25% Background: This assignment is mapped to MLO 1- Solve partial differentiation problems using solver program

Question

MTH61204 Engineering Mathematics I

Assignment 1 (individual) @ 25%

Background:

This assignment is mapped to MLO 1- Solve partial differentiation problems using solver program. Answer all two questions.

Introduction:

This is an individual assignment aiming to use software such as MATLAB as solver program to provide solution for the following two questions. All the answers/steps need to clearly type on the Word/PDF file and paste the “print screen/image” of the MATLAB solution as evidence. The assignment should not exceed 10 pages. Submit the Word/PDF file (only 1 file) into the assignment link in TIMES. Submit the MATLAB file as supplementary file as well in another assignment link labelled as supplementary file.

Please install Matlab campus license, using the student email. Create maths work account after receiving the email. Log in using that account and can download.

https://www.mathworks.com/academia/tah-support-program/eligibility.html

Question 1

Ace toy company has two manufacturing plants (plant A and B), producing spiderman and superman toys. The revenue function for plant A and B in a weekly basis is represented by Eqn Q1a and Q1b, respectively.

??(??, ??) = 100??− 5??²−??³+ 75??− 2??²− 10???? Eqn Q1a

??(??, ??) = 70??− 4??

²+ 30??− 2??²−??3 Eqn Q1b

3

Where, ?? and y representing the numbers of spiderman and superman toy sold, respectively, in the unit of thousand. Meanwhile the revenue function for both plants are in thousand Ringgit Malaysia (RM). List down all the assumptions/values/methods used to solve this question.

Solve for the x and y that can maximize the total revenue (in one week basis) for the Ace toy company by using the solver program and then find the revenue for one year. Compare the answer(s) with manual calculation and draw conclusion. Show the test for relative minima/maxima.

(13 marks)

The Ace toy company projected there will be more units of toys sold in Christmas season, particularly for plant B which is in western country. It is predicted that the numbers of spiderman and superman toys sold by plant B to increase by 3% and 2%, respectively. Approximate the plant B new monthly revenue (for December month) in RM. Show your calculation by using solver program and compare with manual calculation. Draw conclusion on the actual December revenue versus the approximate December revenue for plant B.

(12 marks)

[Q1: 25 marks]

Question 2:

A jelly company produces jelly in cone shape as shown in Figure Q2. You as the boss of the jelly company, would like to redesign the jelly cone that appears to fill more jelly but in actual holds the similar volume of jelly (a standard jelly cone with volume range of 3π to 4π cm³). Solve for the new design dimension of the cone (identify the height and radius) by using the small change differential equation and justify why you think your new design is better. List down all the assumptions/values/methods used to solve this question. Compare the answer between manual and solver program, draw conclusion for your finding(s).

Figure Q2: Jelly filled in cone.

[Q2: 25 marks] Rubric for Assignment 1

Criteria	Weightage	Outstanding (20-25)	Mastering (14-19)	Developing (8-13)	Beginning (0-7)
Q1. Solve partial differentiation problems using solver program	25%	All the calculations and comparisons (SOLVER and manual, actual versus approximate) are presented in clear, precise, and correct manner. All the assumptions/values/methods used are clearly stated and explained, including the conclusions.	Most of the calculations and comparison (SOLVER and manual, actual versus approximate) are presented in clear and correct manner. Most of the assumptions/values/method s used are clearly stated and explained, including the conclusions.	Small portion of the calculations and comparison (SOLVER and manual, actual versus approximate) are presented in unclear or incorrect manner. Missing some of the assumptions/or unclear values/methods used, and partial conclusion is provided. .	Most of the calculations and comparison (SOLVER and manual, actual versus approximate) are not clear or incorrect. Missing some of the assumptions or unclear values/methods used, little to no explanation is given for the conclusions.
Criteria	Weightage	Outstanding (20-25)	Mastering (14-19)	Developing (8-13)	Beginning (0-7)
Q2. Solve partial differentiation problems using solver program	25%	All the calculations and comparisons (SOLVER and manual, new design versus old design), including the justification are presented in clear, precise, and correct manner. All the assumptions/values/methods/ figures used are clearly stated and explained, including the conclusions.	Most of the calculations and comparison (SOLVER and manual, new design versus old design), including the justification are presented in clear and correct manner. Most of the assumptions/values/method s/figures used are clearly stated and explained, including the conclusions.	Small portion of the calculations and comparison (SOLVER and manual, new design versus old design), including the justification are presented in unclear or incorrect manner. Missing some of the assumptions/or unclear values/methods/figure s used, and partial conclusion is provided.	Most of the calculations and comparison (SOLVER and manual, new design versus old design), including the justification are not clear or incorrect. Missing some of the assumptions or unclear values/methods/figures used, little to no explanation is given for the conclusions.