document.write( "Question 1206524: sammy is selling widgets. If he sells 1 widget, it costs him $1 to produce it and he can sell it for $10. If he sells 2 widgets, it costs him $2 to produce 2 widgets, but he can only get $9 for each widget. It costs $1 to produce each widget. The average price decreases by $1 for every extra widget sold. How many widgets should sammy sell to maximise his profit? \n" ); document.write( "

Algebra.Com's Answer #844065 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "sammy is selling widgets. If he sells 1 widget, it costs him $1 to produce it and he can sell it for $10.
\n" ); document.write( "If he sells 2 widgets, it costs him $2 to produce 2 widgets, but he can only get $9 for each widget.
\n" ); document.write( "It costs $1 to produce each widget. The average price decreases by $1 for every extra widget sold.
\n" ); document.write( "ow many widgets should sammy sell to maximise his profit?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Cost producing x widgets is x dollars.\r\n" );
document.write( "\r\n" );
document.write( "Selling price of each one widget in the group of x widgets is 11-x.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So the profit is\r\n" );
document.write( "\r\n" );
document.write( "    P(x) = Revenue(x) - Cost(x) = x*(11-x) - x = -x^2 + 10x.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The maximum of P(x) is at   = \"  \",  where  \"a\"  is the coefficient\r\n" );
document.write( "at  ,  \"b\"  is the coefficient at x.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In this problem,   =  =  = 5.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the optimum number of widgets in group to produce and to sell is 5.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It gives the maximum profit of -5^2 + 10*5 = -25 + 50 = 25 dollars per group.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "On finding the maximum/minimum of a quadratic function see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO complete the square to find the minimum/maximum of a quadratic function\r
\n" ); document.write( "\n" ); document.write( "    - Briefly on finding the minimum/maximum of a quadratic function\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO complete the square to find the vertex of a parabola\r
\n" ); document.write( "\n" ); document.write( "    - Briefly on finding the vertex of a parabola\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );