algebra

Name Simón Solbas Fagernes I.D. Number

Project 2

Evaluation 32

Advanced Algebra 1 (MTHH 039 058)

Be sure to include ALL pages of this project (including the directions and the assignment) when you send the project to your teacher for grading. Don’t forget to put your name and I.D. number at the top of this page!

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Now it is time to complete a Project for this course. Be sure to follow all the directions carefully when completing your Project.

This project contains a possible 100 points and counts for 8% of your final course grade. To complete this project, and submit it electronically, you will need to download and save this editable copy of the project on your computer, complete it using your word processing program, and save it in either .rtf or .doc format for uploading, or print it, complete it on paper, then scan it to either .rtf or .pdf for uploading.

**You may use the equation editor feature or drawing tools in your word processing to complete your project for electronic submission. Please be aware that you are responsible for learning to use these tools and for completing ALL parts of your project prior to submission.**

This project contains activities, as well as questions for you to answer. Follow all the directions carefully. You will not receive all the points possible if you do not answer each question completely. Feel free to add more space or extra pages to this project if you need them.

If you choose to submit your project by mail, see the Mail Submission instructions under the Project Submission link on the online course management system homepage.

Your graphing calculator may be used on this project. You may also use scratch paper to work out the solutions. Be sure to answer each question fully. You may add more space if you need it.

Part A – Linear Programming (possible 20 points)

Do the Linear Programming Activity on page 145 of your textbook.

Use your graphing calculator to work through the 6 steps in the activity to find the maximum or minimum value for our objective function, P. Complete the exercises.

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Part B – Building a Business (possible 20 points)

Do the Building a Business Activity Lab on pages 234-235 of your textbook.

a. Write the inequalities to describe each objective and constraint.

Flavor A’s production in a day = 126kg

Flavor B’s production in a day = 136 kg

1 cocoa bar requires 1.8g Flavor A and 4.0g Flavor B.

1 choco lot requires 2.8g Flavor A and 1.7g Flavor B.

Lets say we will produce x quantity cocoa bar and y quantity of choco bar.

So, 1.8x +2.8y <= 126000 and 4x+1.7y<=136000

And Acc, to mentioned conditions, machine can wrap 50,000 chocolates per day.

So, x+y<=50,000.

Ans: 1.8x +2.8y <= 126000

4x+1.7y<=136000

x+y<=50,000

b. Graph the inequalities you wrote in part a.

c. Find the quantity of each chocolate bar you should manufacture to maximize your daily profit. Calculate the profit you will earn.

To earn maximum profit, maximum resources should be utilized.

1.8x +2.8y <= 126000

4x+1.7y<=136000

x+y<=50,000

To utilize maximum, these equations will become

1.8x +2.8y = 126000

4x+1.7y =136000

x+y<=50,000

Solving, 1st and 2nd equation gives x = 20466, y = 31842…………….1

Solving 2nd and 3rd gives x = 22173, y= 27826…………………………2

Solving 1st and 3rd gives, x=14000, y= 36000…………………………..3

1st ans is not possible, because x+y is becoming greater than 50,000. And machine can pack only 50,000 bars. So possible ans are 2nd and 3rd

Profit = 14x+12y

Putting 2nd in profit equation

Profit = 14*22173 + 12*27826 = 644334

Putting 3rd in profit equation

Profit = 14*14000 + 12* 36000 = 628000

So, profit is maximized when cocoa bar is 22173 and choco-bar is 27826. Profit earned is 644334 cents.

Part C – Modeling Using Residuals (possible 20 points)

Do the Modeling Using Residuals Activity Lab on page 244 of your textbook.

You have learned that there is more than one model for a set of data. You can look at the y-values on the calculator to determine which model is better. When you find these differences, you are looking at the residuals. Residuals that are closer to zero will represent the better model!

Work through the 5 steps in the activity with your graphing calculator. You should see that for this particular problem, the quadratic model is the best.

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Part D – Quadratic Inequalities (possible 20 points)

Do the Quadratic Inequalities Activity Lab on page 296 of your textbook.

Use your graphing calculator to work through activities 1, 2, and 3. Do only problems 1 – 15.

Activity 1:

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Activity 2:

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Activity 3:

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Part E – Pascal’s Triangle (possible 20 points)

Do the Pascal’s Triangle Activity Lab on page 352 of your textbook.

Skip question 7. Answer questions 1-6 and question 8 (NOT question 7).

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Detailed instructions for submitting projects for grading can be found under the Project Submission link on the online course management system homepage and on your Enrollment Information Sheet.