# Project #58311 - math

In this capstone you will be applying some of the algebraic concepts you studied to solve a business problem. For this capstone you will be uploading one MS Word document in the space provided for capstone in module 6. All answers, tables, figures and charts should be presented in one document. Your answers should be typed in Times Roman 12 pts., double spaced and should follow APA format.

Please answer the following questions:

I       In a discussion of producing and selling a product the following terms are used.

·         Fixed Costs

·         Variable Costs

·         Total Costs

·         Revenue

·         Output

·         Break-Even Point

Please explain what each of these terms mean.

II.                  (a) If the fixed cost of producing a product is \$100. If the average variable cost is \$2, and the selling price is \$2.50 per unit, write out the total cost function and the total revenue function (Hint: These are linear equations). Find the break-even output level (Hint: Total Revenue = Total Cost).

(b)   Complete the following tables for different levels of output:

 Output 0 50 100 150 200 250 300 350 400 Fixed Cost Variable Cost Total Cost

 Output 0 50 100 150 200 250 300 350 400 Price per unit Total Revenue
 Output 0 50 100 150 200 250 300 350 400 Total Profit

© In Excel draw the line for the profit data above. Find the break-even level of output. Verify that the break-even level of output is the same as in (a)

III.                (a) The average variable cost is not always a constant. Sometimes suppliers may give a huge discount for large orders, which would make the average variable costs decrease as output increases. For example, if the average cost is 2 – 0.001 q, then you will see that the variable cost decreases as output increases. Assuming again that the fixed cost is \$100 and the selling price is \$2.50 per unit complete the following tables:

 Output 0 50 100 150 200 250 300 350 400 Fixed Cost Variable Cost Total Cost

 Output 0 50 100 150 200 250 300 350 400 Price per unit Total Revenue
 Output 0 50 100 150 200 250 300 350 400 Total Profit

(b) In Excel draw the line for the profit data above. Find the break-even level of output.

© Given the information in (a), write out the cost function, revenue function and profit function. Algebraically, using the profit function, find the break-even output. Verify that the break-even output is the same as that obtained in (b).

IV.                (a) Sometimes if there is a shortage of raw materials the average variable costs may increase as output increases. If the average cost is 2 + 0.001 q, then you will see that the variable cost increases as output increases. Assuming again that the fixed cost is \$100 and the selling price is \$2.50 per unit complete the following tables:

 Output 0 50 100 150 200 250 300 350 400 Fixed Cost Variable Cost Total Cost

 Output 0 50 100 150 200 250 300 350 400 Price per unit Total Revenue
 Output 0 50 100 150 200 250 300 350 400 Total Profit

(b) In Excel draw the line for the profit data above. Is there a break-even level of output?

© Given the information in (a), write out the cost function, revenue function and profit function. Algebraically, using the profit function, find the break-even output. Verify that the answer is the same as that obtained in (b).

V.           Conclusion: Briefly explain the answers obtained in this capstone. Are there any other application in Economics, Finance and Accounting that you think linear and quadratic functions can be used? Give examples.

 Subject Mathematics Due By (Pacific Time) 02/16/2015 11:41 pm
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