document.write( "Question 1185004: Suppose that a manufacturer will place 1000 units of a product on the market when the price is $10 per unit, and 1400 units when the price is $12 per unit. Find the supply equation for the product assuming the price p and quantity q are linearly related. \n" ); document.write( "

Algebra.Com's Answer #815772 by ikleyn(52799) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Suppose that a manufacturer will place 1000 units of a product on the market when the price is $10 per unit,
\n" ); document.write( "and 1400 units when the price is $12 per unit.
\n" ); document.write( "Find the supply equation for the product assuming the price p and quantity q are linearly related.
\n" ); document.write( "~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "The equation for supply is of the form  \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    q = c + d*p,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "where q is the quantity of items, produced and sold, while p is the price for single unit of production.\r\n" );
document.write( "\r\n" );
document.write( "\"c\" and \"d\" are coefficients; in our consideration, they assumed to be constant.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You can approach this problem formally.  You have a straight line and two given points in it, (10,1000) and (12,1400),\r\n" );
document.write( "\r\n" );
document.write( "and your task is to construct the appropriate linear function.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then you write the standard interpolation-extrapolation equation\r\n" );
document.write( "\r\n" );
document.write( "    q =  + \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "and substitute there  given values  = 10,   = 12,  = 1000,   = 1400.  You will get then\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    q = 1000 +  = 1000 +  = 1000 + 200*(p-10),\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "so the final form of your supply equation is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    q = 1000 + 200*(p-10),   or, EQUIVALENTLY,  q = 200p - 1000.      ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );