top-rated free essay

Add Math Sba

By Jabari1 Apr 20, 2015 501 Words
Innovating new packaging by determining the best suitable level of efficiency with the use of calculus for Trini Chocolate Delights.

JABARI BOWMAN
ADD MATH
SBA
CLASS: 5-6
SCHOOL: ST. MARY’S COLLEGE
TEACHER: MR. YIP-YOUNG

Problem Statement
The project’s purpose is to work out the best level of production to suit the new packaging for ‘Trini Chocolate Delights ltd.’ The company’s objective is to maximize produce of their new product but minimize manufacturing cost. To fulfill this task the use of calculus is needed along with other mathematical methods to help design a best suitable and cheap packaging that will be used to carry a grand amount of smaller products while cost remain in a stead/safe amount.

Mathematical Formulation

Below is a list of formulas applied to each question

A. Tan =
-

B. Substitution
Area of triangle + Area of rectangle= Area of pentagon

C. Differentiation

D. The quadratic equation

The quadratic formula

OR
Factorization of the quadratic formula

E.

Problem solution

A Problem diagram


E B

ycm

D 8xcm C

i) F is the mid-point of line EB and it’s also the perpendicular of triangle EAB. The line AF cuts triangle EAF in half resulting in two isosceles triangles. Since AFB= AFE and DC=EB, then FB and EF are both equal to 4xcm. , , then

Therefore

ii) Since the total cross-sectional area is 90cm then:
(i)

(ii)

Make y the subject in equation (i)

Now sub (i) into (ii)

Maximum area

When x=3 the maximum area:

Therefore the maximum cross-sectional area is 540

When the equation is divided by 60 it becomes:

Therefore

These are the two possible values of x that satisfies the maximum cross-sectional area being 300

X Value
0
1
2
3
4
5
6

0
300
480
540
480
300
0

Prism length=5cm
x=1
Since x=1, cross-sectional area=300 and cross-sectional perimeter=90cm Volume of prism=
=

When the sides of the container is opened up it makes a net consisting of 7 faces, 2 pentagonal faces and 5 rectangular faces.

Length=Cross-sectional perimeter=90cm
Width=prism length=5cm

Therefore

Area of rectangles=590
=450

Total surface area (sum of the areas of each face) = Cross-sectional area+ area of rectangles =300(2) +450
=1050

Fixed costs=$6000
Variable costs= and
Average costs (AC) =

For average cost to be a minimum

X=600{Therefore 600 units has to be produced to maintain average cost at its minimum level.}

Since x=600 gives a minimum value

Application of Solution
Since x (the number of units produced) is equaled to 600, the average cost of the product using the formula:

Therefore the possible minimum average cost is $25 per unit

Conclusion

It was determined that the Trini Chocolate delights ltd. had to produce 600 units at the minimum average cost of $25 per tin of chocolates. Also the maximum cross-sectional area was determined to be 300 if the value of x was either 5cm or 1cm.

Cite This Document

Related Documents

  • Add Maths Sba

    ...Ruel Wallace Add Maths S.B.A Mr. Teesdale 5-8 Table of Contents Cover page……………………………………………………………………………………………1 Table of contents………………………………………………...

    Read More
  • add math project

    ...Introduction Obesity can lead to various health problems. My school has decided to carry out a “Healthy Lifestyle Campaign” with the aim to create awareness among students about obesity-related health problems. The Body Mass Index (BMI) gives an indication of the physical state of person as being underweight, normal, overweight or obe...

    Read More
  • Add Maths SBA Insecticide

    ... VANSA DOOKERAN Additional Mathematics SBA School Based Assessment Vansa Dookeran 5X TABLE OF CONTENTS Page # Project Title 3 Purpose of Project 3 Method of Data Collection 4 Presentation of Data 6 ...

    Read More
  • Math

    ... The case between Beauty and Stylish involves concept of a valid contract, pre-contractual statements, express term and misrepresentation. A valid contract is established between Beauty and Stylish when an offer is accepted and there is intention for both parties to create legal relations. An offer refers to the expression of willingness of t...

    Read More
  • Add Math Folio 2013

    ...SMK CONVENT BATU PAHAT JEB: 0017 ADDITIONAL MATHEMATICS PROJECT WORK 2013 THE HOUSEHOLD EXPENDITURE SURVEY (HES) NAME : KUA YU CHAN I/C NO. : EXAM REGISTRATION NO: JA017K016 GROUP MEMBERS: 1) KUA YU CHAN 2) DHARSHINI A/P NEELA MEHAN 3) LIM HUI LING 4) SHEE HUI CHIEN 5) REGINA LEONG ZHI LING OBJECTIVES We...

    Read More
  • Add Maths Project Work

    ...PROJECT WORK FOR ADDITIONAL MATHEMATICS 2012 POLYGONS IN OUR LIFE Name: Class: Teacher: I/C number: CONTENT |No. |Title |Pages | |1 |Objectiv...

    Read More
  • Add Mahs Sba

    ...Brandon Deonath Add maths SBA Mrs. Ramnarine 5s Title: To find the maximum volume of a box using the method of differentiation. Problem statement: Mr. Lee, owner of a private cake company, sells a square 5 inch cake in a box made from 50 x 50 cm sheets of material. He would like to put a bigger square 8 inch cake in a box made from th...

    Read More
  • Add Maths Projek

    ...performance of your class. Give your reasons. (c) Measure of dispersion is a measurement used to determine how far the values of data in a set of data are spread out from its average value. Explain the advantages of using standard deviation compared to interquartile range as the better measure of dispersion. 4. Ungrouped data and grouped data ha...

    Read More

Discover the Best Free Essays on StudyMode

Conquer writer's block once and for all.

High Quality Essays

Our library contains thousands of carefully selected free research papers and essays.

Popular Topics

No matter the topic you're researching, chances are we have it covered.