mat 117 appendix C (brand new)
mat 117 appendix C (brand new)
CSU - Dominguez hills
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Date Created: 11/16/15
Axia College Material Polynomials Appendix C 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 pi 2 mil l lit Putting the atmes tn the aquattu paints we lll j Slim 2n mtg lfi 1 m mm El 2 2n mtg 1 1u mist 1 lit them 2D 2 42m l lit n1ti 52m is I 2 l1l39m MAT 117 m 2 11 h m 2 1 put the l t 39 Inf m in BWEJIi get the l 39 elf it 1E 2 THEE l Iii 1B 2 1352 1 I 2 52 l h 1H 2 52 2 h El 2 h thE t Ef i E the HELMET is p 2 I l El 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 H H2 EEH revenue equation Provide your answer in simplified form 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 If b represents a fixed cost what value would represent b h 1 I fitted d find the cost equation for the tile Write your answer in the form C mx b mt hle BEST m tttitii ttmttl was per tile m 2 E umtt tle casts therefute cast equatimr far 21 tiles ts gimmert i513 Elias 2 Ea l SHE East is in damn3 The profit made from the sale of tiles 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 Profit 2 RtE E E Casts MAT 117 Hewetttee 2 t3 t Elan feet 2 Ex S Thetefet39e pt ezf tt P P 2 E2 EEK EBB P I2 EEK x S l P 2 t3 El x S i Pt39eftt is in d f What is the profit made from selling 20 tile sets per month Putting x 20 we get profit as P Jr39 55K see P 2 2l393l EJEIIEEEI SHE P 2 1 lil39 l Ill l S l P 2543 g What is the profit made from selling 25 tile sets each month Puttt g t 25 we get preftt es P 2 I3 l El x EDIE P 2 25113 516253 SHE P 2 EEEJ l 14li REID P zine h What is the profit made from selling no tile sets each month lnterpret your answer Puttt g t 1quot we get P 2 t3 3 El x S i P 2 lll E EJEEEEI SHEquot P 2 ll li EDIE P 2 3lilI Therefeee eemptmywt he in legathts eeet t3 the fitted eelst i Use trial and error to find the quantity of tile sets per month that yields the highest profit For a quadratic equation with a negative leading coefficient there is always a maximum value at the vertex which is located on the equation39s Axis of Symmetry m7 lip 55 I Ef gy Ell I Em 3 I 1953 3 I Ef gy 3 Fettex f the eqtetttttm t3 gi 39 MAT 117 I E SE 3 2 2E j 2 I3 EJEK SHE y 2 E l EJEEEJEJ 300 y 2 1 1553 300 y 2 154 I F3 1 3335 j How much profit would you earn from the number you found in part i P 2 I2 t 516x 300 P 2 2 3 SEES 30039 P 2 la l 1563 310039 P 5 E l Therefore mmin profit 2 I Etlu k What price would you sell the tile sets at to realize this profit hint use the demand equation from part a Prim for the tile is gimmert EL39E39 P 2 r 152 P 13 52 Prime pier tile 1 34 2 The break even 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 break even values Puttth ti r3 i 5511 310039 2 t 1 3 5531 1 3100 2 it 302 151llx JE1 1 310039 2 lI x E x 2 if x 2 E m39x 2 E The company will break even if they sell 50 sets or 3 sets of tiles 3 In 2002 Home Depot s sales amounted to 58200000000 In 2006 its sales were 90800000000 a Write Home Dethss 2002 sales and 2006 sales in scientific notation 2003582 in mm MAT 117 entitieeee e 10m 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 b What was the percent growth in Home Depot s sales from 2002 to 2006 Do all your work by using scientific notation It iet eeee in heme seies 2 ate it 10m eee e 101 325 e we it ieteeee weeiti tie the immense ti ieitieti the starting peth ENE times ii 335 he 11 aee e 10m Sil i39lq i t h 39 er ehettt e 55 itiet39eeee H 1lilI 2 sl l l 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 pieces of PVC plumbing pipe be MAT 117 How long is the PVC lt pipe 8 feet 12 feet MAT 117
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