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Math 1090.04 Homework 03 Spring 2013 Name O(.LdiOflS Student ID Number: Instructions: Each student is expected to follow the Homework Guidelines described on the course webpage • Solve the Part A Problems on your own paper. • Solve the Part B problems in this handout. • Attach this handout to the front of your homework assignment Reading Assignment: • Chapter 1.5 • Chapter 1.6 - - Text pages 41-26 Text pages 49-56 Part A: • Chapter 1.5 Text pages: 46-48 Problems: 11-20, 21-25, 31-40, 41-44, 46-47, 50-56, 67-70, 71-74 - • Chapter 1.6 Text pages: 57-60 Problems: 1, 3, 5, 7, 8, 9, 11-14, 16-17, 20, 23, 28 - •0 ctj C C.) hO CD a) C CJD .hO — an C C j5 a) C - C.) C C) C 0’ C N 0’ Cl) C Cl) 0) 0) 0) I54 ij li — - ,& çTo 4 . -t % C) oco TI f1 1- ci i K C.) 00 - 0° —ii I -d x 1 LJ cO\ c-j-çç I )( II j!± cx If) •r...t “I • (I) 11) ho c’1 —I C a) - an C) Ti Co “ —1 If) I) hO rfl -, \ (C LC C) 0 c) C b cD E C lD II :i: - biD o 0 a Al ‘I (1 jN it Al 4:.:n .4 ‘41 th M I \%)< -J t ‘E “ ‘c 0 — U) >( 4 c !iI 0 - 11 i) ,j, —k—) as [I2 -D C C) . - - — C — ci) ci)— I - U I 0 ci ci Li I’ cO -‘I I’ a c’4 ft < o ? — C C c%J - + F. - 0 Homework 03, Page 4 of 10 MathlO9O.004 30 January 2013 Chapter 1.6: Business Applications 4. Concert promoters are willing to sell tickets at a price of $8 each if they can sell 6040 tickets; however, if they can only sell 6250 tickets they insist on charging $50 each. At. the same time, 7250 music fans are willing to purchase a ticket for $10 each, hut only 7000 fans are willing to purchase a ticket if they are $20 each. (a) Find the Demand equation described by this scenario: on cLiscr Its - J 1 L (21fl sujiurs C cu-ca U)’ Rmni b€ (Z5O10 Jb rn z-S — jJz6 0 = • - p z’50 (‘ StDp (io - 2S - C,’ 2 k3O L - (b) Find the Supply equation described by this scenario: — pI SC’fl Spp a. - : ; nt (o1 &zso(1t) 2. (lO S 2.10 N OLfl -S1p : (p - () (> 2- — zc C 30 January 2013 Homework 03, Page 5 of 10 vIath 1090.004 (c) Estimate the market eciuilibriiim by graphing the supply and demand ecluations on the same graph. LI -----p / — I 1 / — - ---. ---. ] ‘S / 7_ — — - -- / -- Figure 1: Problem 4 Record your estimate here: / CjsLn -- / C U C-) 0 0 — —jco 7 \ 1 Q t1 r1 Nl k — I’ 0 o 4’ 0 N ..-c C c-o ç)r 0 0 0 .‘.i 0 / ‘ - 0 o ‘‘% _ll - 0 0 N i U Homework 03, Page 7 of 10 MathlO9O.004 30 January 2013 5. A gasoline station has weekly costs and revenue (the money taken in by the station) that are functions of the number of gallons of gasoline purchased and sold. If x gallons are 1.2x + 1080 and weekly revenue purchased and sold, weekly costs are given by C() by R(x) = 1.6r (a) What are the fixed costs? What does this number tell you? Q31 0 fr Is Oh fl fl ô 7t t1flAflhi jas c/d’. (b) What are the variable costs? What does this number tell you? , Ofl 7u Oh I ) s r pc LLLer (c) What is the marginal profit? What does this number tell you? i. & • P(x - r /2 /oo7 O-4X —/o80 • niizJ pio-f-i O. 10 per SaJLon n a cç vJ, J (d) What is the marginal revenue? What does this number tell you? Oh ; In t • &hI - J p/fo - ‘.& S-ti//S I, Co )-Lt S 3 it17O17 jl1 Z’7-6 puó/i’cjôr. (e) What is the profit from selling 100 items? How would you interpret this solution? .41/00) O S Oj —/oo J)ôo 90 /a //5S flWJ / I = Lt LJf5 O/7& /0 0 I Homework 03, Page 8 of 10 Math 1090.004 30 January 2013 (f) What is the profit from selling 1000 items? Comparing this to (e), how would you interpret the answer? A(fooO) iOO v(/ood) -Ief t L LjhLt- 1i& SflLO OfltJ sfi /J OO /flpjf /O -(O J ; /00 (g) Graph the appropriate equations to estimate the break even point (Hint: Convert decimals to fractions) C Figure 2: Problem 5 C ath1O9OOO C (h) Calculate the breakeven point - 0.4 x -IO (oo C 4X /(2oo) CCC) €L)Cfl Pont = 43zo (oo, 43o I I (i) How does your calculated break-even point compare to your estimate? If they are different can you explain why? •1 Homework 03, Page 10 of 10 MathlO9O.004 30 January 2013 * 6. Extra Credit Challenge: You drew a graph in the problem above to estimate the break even point there is another graph you can draw to come up with the same esti mate What is it? - - If you figure it out: Include your graph and compare this estimate to your actual solution and your previous estimate. —. — .— In —1v — -— a 777 Figure 3: Problem 6 C