1105_LW3_solutions_F11

1105_LW3_solutions_F11 - MACHOS Lecture Worksheet 3...

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Unformatted text preview: MACHOS Lecture Worksheet 3 Sections 3.1-3.3 Fall, 2011 1. The manager of a 200-unit apartment complex knows from experience that she can rent every unit if the rent is $700 per month, but on average, one unit will remain unrented for each $10 increase in the rent. Examine the table before proceeding. # of$10 " increases Monthly Rent ($) # of units rented Total Monthly Revenue ($) R(x) x 700 + 10(0) = $700 200 - 0 = 200 (700)(200) = $140,000 1 700 + 10(1) = $710 200 - 1 = 199 (710)(199) = $141,290 2 700 + 10(2) = $720 200 - 2 = 198 (720)(198) = $142,560 50 700 + 10(50) = $1200 200 - 50 = 150 (1200)(150) = $180,000 100 700 + 10(100) = $1700 200 - 100 = 100 (1700)(100) = $170,000 199 700 + 10(199) = $2690 200 -199 = 1 (2690)(1) = $2690 200 700 + 10(200) = $2700 200 - 200 = 0 (2700)( 0) = $0 a) Complete the table below by writing expressions that represent the monthly rent, the number of units rented, and the revenue when the rent is raised by 100 dollars x times. __ x _---'--1_7 D_o_t-_l ()_X__ 2_oo_-_x __ 1 R(x) ~ G" + I(( )(200-X') b) Sketch the graph of the quadratic revenue function R(x). Find both coordinates of the maximum point, and interpret this point in context. R(~,::: (7 0+10XX200-)() 1- RlX) =- fttOOOO +- 1'300 X.-)0 X- L ( 1 3 0 0 7 \ Ve(~x- 2("'\0) ~) ve\"teX (~5"J \ ~2. 'L;O) t R(~5')=1 ~ 1 2 5 D .-r:f ,""e.- VV\().~~t'" r~\ ~e..s~-relAt b j .t o StxJ~-.p, ve: _ +i~e.S rnoV\t\A\1. ~~t w.l\ 10 e. ~ ~ 3 So /"1\ I>~ fk Q..V\.J. v--e."e.t'\ c,e, ~.;,If Monthly Revenue ($) y 200,pOO...
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1105_LW3_solutions_F11 - MACHOS Lecture Worksheet 3...

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