Math117 Appendix C
Math117 Appendix C
CSU - Dominguez hills
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Date Created: 11/16/15
Axia College Material Appendix C Polynomials Retail companies need to keep close track of their operations in order to maintain profitability Often the sales data of each individual product is analyzed separately which can be used to help set pricing and other sales strategies Application Practice Answer the following questions Use Equation Editor to write mathematical expressions and equations First save this file to your hard drive by selecting Save As from the File menu Click the white space below each question to maintain proper formatting 1 In this problem we will analyze the profit found for sales of decorative tiles A demand equation sometimes called a demand curve shows how much money people would pay for a product depending on how much of that product is available on the open market Often the demand equation is found empirically through experiment or market research a Suppose that a market research company finds that at a price of p 20 they would sell x 42 tiles each month If they lower the price to p 10 then more people would purchase the tile and they can expect to sell x 52 tiles in a month s time Find the equation of the line for the demand equation Write your answer in the form p mx b Hint Write an equation using two points in the form xp 42 20 52 10 m 20 1042 52 m 1010 m1 y 10 1X 52 y 10X52 yX62 pX62 A company s revenue is the amount of money that comes in from sales before business costs are subtracted For a single product you can find the revenue by multiplying the quantity of the product sold x by the demand equation p b Substitute the result you found from part a into the equation R xp to find the revenue equation Provide your answer in simplified form MAT 117 R XX 62 R X2 62X The costs of doing business for a company can be found by adding fixed costs such as rent insurance and wages and variable costs which are the costs to purchase the product you are selling The portion of the company s fixed costs allotted to this product is 300 and the supplier s cost for a set of tile is 6 each Let x represent the number of tile sets c H b represents a fixed cost what value would represent b b 300 d Find the cost equation for the tile Write your answer in the form C mx b C 6X 300 The profit made from the sale of les is found by subtracting the costs from the revenue e Find the Profit Equation by substituting your equations for R and C in the equation P R C Simplify the equation P X2 62X 6X 300 PX262X6X300 P X2 56X 300 f What is the profit made from selling 20 tile sets per month P X2 56X 300 P 202 5620 300 P 400 1120 300 P 420 g What is the profit made from selling 25 tile sets each month P X2 56X 300 P 252 5625 300 P 625 1400 300 P 475 h What is the profit made from selling no le sets each month Interpret your answer P X2 56X 300 P 02 560 300 P 0 0 300 P 300 MAT 117 i Use trial and error to find the quantity of tile sets per month that yields the highest profit P x2 56X 300 P 502 5650 300 P 2500 2800 300 P 0 There is no profit when you sell 50 tile sets P x2 56X 300 P 302 5630 300 P 900 1680 300 P 480 There is a pro t of 480 when you sell 30 tile sets P x2 56X 300 P 352 5635 300 P 1225 1960 300 P 435 There is a pro t of 435 when you sell 35 tile sets P x2 56X 300 P 272 5627 300 P 729 1512 300 P 483 There is a pro t of 483 when you sell 27 tile sets P x2 56X 300 P 282 5628 300 P 784 1568 300 P 484 There is a pro t of 484 when you sell 28 tile sets P x2 56X 300 P 292 5629 300 P 841 1624 300 P 483 There is a pro t of 483 when you sell 29 tile sets The quantity of tile sets per month that yields the highest profit is 28 MAT 117 j How much profit would you earn from the number you found in part h P X2 56X 300 P 282 5628 300 P 784 1568 300 P 484 Pro t from 28 tile sets is 484 k What price would you sell the tile sets at to realize this profit hint use the demand equation from part a pX62 p2862 p34 To realize this pro t I would sell the tile sets at 34 2 The breakeven values for a profit model are the values for which you earn 0 in profit Use the equation you created in question one to solve P 0 and find your breakeven values 0 X2 56X 300 0 X 6X 50 m60 X6 X6 X500 X50 X650 The breakeven values are 6 and 50 3 In 2002 Home Depot s sales amounted to 58200000000 In 2006 its sales were 90800000000 a Write Home Depot s 2002 sales and 2006 sales in scientific notation 2002 Sales 582 x 1010 2006 Sales 908 X 1010 You can find the percent of growth in Home Depot s sales from 2002 to 2006 follow these steps 0 Find the increase in sales from 2002 to 2006 c Find what percent that increase is of the 2002 sales MAT 117 b What was the percent growth in Home Depot s sales from 2002 to 2006 Do all your work by using scientific notation 908 X 1010 582 X 1010 326 X 1010 326 X 10 582 X 1010 5601 5601 X 100 5601 56 increase source Home Depot Annual Report for FY 2006 httpwww6homedepotcomannualreportindexhtml 4 A customer wants to make a teepee in his backyard for his children He plans to use lengths of PVC plumbing pipe for the supports on the teepee and he wants the teepee to be 12 feet across and 8 feet tall see figure How long should the PVC plumbing pipe be How long is the PVC lt pipe 8 feet l W 12 feet 6282H2 36 64 H2 100H2 H 100 H10 MAT 117 The length of the PVC pipe is 10 feet MAT 117
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