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A company manufactures and sells blank audiocassette tapes.
\n" ); document.write( " The weekly fixed cost is $5,000 and it costs $0.60 to produce each tape.
\n" ); document.write( " The selling price is $2.00 per tape.
\n" ); document.write( " How many tapes must be produced and sold each week for the company to generate a profit?
\n" ); document.write( ":
\n" ); document.write( "Let x = no. of tapes produced
\n" ); document.write( ":
\n" ); document.write( "The cost to produce these tapes would be:
\n" ); document.write( "C(x) = .60x + 5000
\n" ); document.write( ":
\n" ); document.write( "The revenue from the sales of these tapes which sell for $2, would be:
\n" ); document.write( "R(x) = 2x
\n" ); document.write( ":
\n" ); document.write( "We know to make a profit, revenue has to exceed the costs, right?
\n" ); document.write( "R > C
\n" ); document.write( "replacing these with the equations we have find x
\n" ); document.write( "2x > .60x + 5000
\n" ); document.write( "2x -.6x > 5000
\n" ); document.write( "1.4x > 5000
\n" ); document.write( "x >
\n" ); document.write( "x > 3571.4, has to be an integer, round it up so we have
\n" ); document.write( "x = 3572 tapes will produce a slight profit
\n" ); document.write( ";
\n" ); document.write( ":
\n" ); document.write( "Prove that
\n" ); document.write( "R = 2(3572) = $7,144.00
\n" ); document.write( ":
\n" ); document.write( "C = .6(3572) + 5000
\n" ); document.write( "C = 2143.20 + 5000
\n" ); document.write( "C = $7,143.20
\n" ); document.write( ":
\n" ); document.write( "revenue exceeded cost by 80 cents!
\n" ); document.write( ":
\n" ); document.write( "You can see, when 3572 (or more) tapes are produced, a profit will be made
\n" ); document.write( ":
\n" ); document.write( "Did this make sense to you? \n" ); document.write( "