document.write( "Question 402399: The cost (in thousands of dollars) for making x snow blowers is given by the function: C(x)= 200 + 60x
\n" ); document.write( "The revenue (in thousands of dollars) is given by the function:
\n" ); document.write( " R(x)= 90x-x^2
\n" ); document.write( "a) write and simplify a function P that represents the profit (in thousands of dollars) in terms of x.
\n" ); document.write( "b) Find the number of snow blowers that would produce a zero profit.
\n" ); document.write( "c) What is the profit for selling 18 snow blowers? \n" ); document.write( "

Algebra.Com's Answer #284649 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"P%28x%29+=+R%28x%29+-+C%28x%29\"$
\n" ); document.write( " $\"P%28x%29+=+90x+-+x%5E2+-+%28200+%2B+60x%29\"$
\n" ); document.write( " $\"P%28x%29+=+90x+-+x%5E2+-+200+-+60x\"$
\n" ); document.write( "(a)
\n" ); document.write( " $\"P%28x%29+=+-x%5E2+%2B+30x+-+200\"$
\n" ); document.write( "(b)
\n" ); document.write( " $\"0+=+-x%5E2+%2B+30x+-+200\"$
\n" ); document.write( "use the quadratic formula
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"a+=+-1\"$
\n" ); document.write( " $\"b+=+30\"$
\n" ); document.write( " $\"c+=+-200\"$
\n" ); document.write( " $\"x+=+%28-30+%2B-+sqrt%28+30%5E2-4%2A%28-1%29%2A%28-200%29+%29%29%2F%282%2A%28-1%29%29+\"$
\n" ); document.write( " $\"x+=+%28-30+%2B-+sqrt%28+900+-+800+%29%29%2F%28-2%29+\"$
\n" ); document.write( " $\"x+=+%28-30+%2B-+sqrt%28+100+%29%29%2F%28-2%29+\"$
\n" ); document.write( " $\"x+=+%28-30+%2B+10%29%2F%28-2%29+\"$
\n" ); document.write( " $\"x+=+10\"$
\n" ); document.write( "and
\n" ); document.write( " $\"x+=+%28-30+-+10%29%2F%28-2%29+\"$
\n" ); document.write( " $\"x+=+20\"$
\n" ); document.write( "there is zero profit for selling 10 or 20 snowblowers
\n" ); document.write( "(c)
\n" ); document.write( "For selling 18 snowblowers:
\n" ); document.write( " $\"P%28x%29+=+-x%5E2+%2B+30x+-+200\"$
\n" ); document.write( " $\"P%2818%29+=+-18%5E2+%2B+30%2A18+-+200\"$
\n" ); document.write( " $\"P%2818%29+=+-324+%2B+540+-+200\"$
\n" ); document.write( " $\"P%2818%29+=+16\"$
\n" ); document.write( "There is $16K profit for selling 18 snowblowers
\n" ); document.write( "---------------
\n" ); document.write( "Note that you can see the whole picture by plotting $\"P%28x%29\"$
\n" ); document.write( " $\"+graph%28+300%2C+300%2C+-5%2C+30%2C+-5%2C+30%2C+-x%5E2+%2B+30x+-+200%29+\"$
\n" ); document.write( "Note that there is no profit for selling 10 or less snowblowers
\n" ); document.write( "or 20 or more snowblowers \n" ); document.write( "

\n" );