document.write( "Question 274917: Maximizing Revenue: A large hotel is condidering giving the following froup discount on room rates: the regular price of $120 decreases by $2 for each room rented. For example, one room costs $118, two rooms cost $116 x 2=$232, three rooms cost $114 x 3=$342 and so on. a)Write a formula for a function R that gives the revenue for renting x rooms. b)Sketch a graph of R. What is a reasonable domain? c)Determine the maximum revenue and the corresponding number of rooms rented. \n" ); document.write( "
Algebra.Com's Answer #200608 by ankor@dixie-net.com(22740)\"\" \"About 
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A large hotel is considering giving the following group discount on room rates:
\n" ); document.write( " the regular price of $120 decreases by $2 for each room rented.
\n" ); document.write( ":
\n" ); document.write( " a)Write a formula for a function R that gives the revenue for renting x rooms.
\n" ); document.write( "x = no. of rooms
\n" ); document.write( "Rev = no. of room * price of each room
\n" ); document.write( "R(x) = x(120 - 2x)
\n" ); document.write( "R(x) = -2x^2 + 120x
\n" ); document.write( ":
\n" ); document.write( "b)Sketch a graph of R.
\n" ); document.write( "A graph of this equation
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-20%2C+80%2C+-500%2C+2500%2C+-2x%5E2%2B120x%29+\"
\n" ); document.write( ":
\n" ); document.write( "What is a reasonable domain?
\n" ); document.write( "easy to see it would be from 1 to 60 rooms (x)
\n" ); document.write( ":
\n" ); document.write( " c)Determine the maximum revenue and the corresponding number of rooms rented.
\n" ); document.write( "You see this from the graph, but we can find it using the axis of symmetry and vertex
\n" ); document.write( "y = -2x^2 + 120x; where a= -2; b = 120
\n" ); document.write( "x = \"%28-120%29%2F%282%2A-2%29\"
\n" ); document.write( "x = +30 rooms rented would give max revenue
\n" ); document.write( ":
\n" ); document.write( "Find the vertex
\n" ); document.write( "y = -2(30^2) + 120(30)
\n" ); document.write( "y = -2(900) + 3600
\n" ); document.write( "y = -1800 + 3600
\n" ); document.write( "y = $1800 max revenue:
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Confirm this
\n" ); document.write( "room cost: 120-2(30) = 60; then 30 * 60 = $1800 \n" ); document.write( "
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