document.write( "Question 696081: The price P (in dollars) that a radio manufacturer is able to charge for a radio is given by P =40-4x^2 where x is the number (in millions) produced. It costs the company $15 to make a radio.
\n" ); document.write( "a.) Write an expression for the company's total revenue in terms of x (Could you explain the process for finding this expression?)
\n" ); document.write( "b.) Write a function for the company's profit P by subtracting the total cost to make x radios from the expressions in Part A(the one just found)
\n" ); document.write( "c.) Currently, the company produces 1.5 million raidos and makes a profit of $24,000,000. Write and solve an equation to find a lesser number of radios that the company could sell and still make a profit.
\n" ); document.write( "d.) Do all the solutions in part c make sense in this situation? Explain.
\n" ); document.write( "----
\n" ); document.write( "Sorry for the long word problem, but I would appreciate it if someone responds
\n" ); document.write( "Thank You \n" ); document.write( "
Algebra.Com's Answer #428798 by ankor@dixie-net.com(22740)\"\" \"About 
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The price P (in dollars) that a radio manufacturer is able to charge for a radio is given by P =40-4x^2 where x is the number (in millions) produced.
\n" ); document.write( " It costs the company $15 to make a radio.
\n" ); document.write( ":
\n" ); document.write( "a.) Write an expression for the company's total revenue in terms of x (Could you explain the process for finding this expression?)
\n" ); document.write( ":
\n" ); document.write( "Revenue = no. of radios sold * price of the radio
\n" ); document.write( "R(x) = x(40-4x^2)
\n" ); document.write( "R(x) = -4x^3 + 40x
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "b.) Write a function for the company's profit P by subtracting the total cost to make x radios from the expressions in Part A(the one just found)
\n" ); document.write( ":
\n" ); document.write( "Profit = Revenue - the total cost, (15x is the cost of all the radios sold)
\n" ); document.write( "P(x) = -4x^3 + 40x - 15x
\n" ); document.write( "P(x) = -4x^3 + 25x
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "c.) Currently, the company produces 1.5 million radios and makes a profit of $24,000,000.
\n" ); document.write( " Write and solve an equation to find a lesser number of radios that the company could sell and still make a profit.
\n" ); document.write( ":
\n" ); document.write( "Assume they make 1 million radios,
\n" ); document.write( " equation is in millions of radios and millions of dollars
\n" ); document.write( "P(x) = -4x^3 + 25x
\n" ); document.write( "x = 1 (million)
\n" ); document.write( "P(x) = -4(1^3) + 25(1)
\n" ); document.write( "P(1) = -4 + 25
\n" ); document.write( "P(x) = $21 million in profit when they make 1 million radios
\n" ); document.write( ";
\n" ); document.write( "d.) Do all the solutions in part c make sense in this situation? Explain.
\n" ); document.write( ":
\n" ); document.write( "Graphically we can explain it easily,
\n" ); document.write( " y = millions of dollars profit, x = millions of radios sold
\n" ); document.write( "Green line is $21 million
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-2%2C+4%2C+-10%2C+30%2C+-4x%5E3%2B25x%2C+21%29+\"
\n" ); document.write( "Looks like max profit occurs when 1.5 million are sold, do you agree? \n" ); document.write( "
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