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Fab Jeans presently sells ladies' jeans at an average price of $50 a pair,with sales averaging 300 pairs daily. From an analysis of the market, it is estimated that with every $1.50 decrease in the cost of a pair of jeans, daily sales will increase by 25 pairs.
\n" ); document.write( "What price should Fab Jeans change to maximize their daily revenue ? What is the maximum revenue ?
\n" ); document.write( "Let \"x\" be the number of decreases of $1.50:
\n" ); document.write( "Revenue = price*# of sales
\n" ); document.write( "Revenue = (50-1.5x)(300+25x)
\n" ); document.write( "Simplify:
\n" ); document.write( "Rev = 15000+1250x-450x-37.5x^2
\n" ); document.write( "Rev = -37.5x^2+800x+15000
\n" ); document.write( "Maximum Revenue occurs when x=-b/2a = -800/-75 = 10 2/3
\n" ); document.write( "Rounding up: closest to max occurs when x = 11
\n" ); document.write( "That price would be 50-11*$1.5 = $33.50
\n" ); document.write( "Revenue at that price would be $19,266.67
\n" ); document.write( "--------------------------------
\n" ); document.write( "If it costs Fab Jeans $12 to make each pair of ladies jeans, what price should the company charge in order to make the greatest profit ?
\n" ); document.write( "----------------
\n" ); document.write( "# of jeans sold when Rev is max is 300+25x = 300+25*11 = 575
\n" ); document.write( "If each one costs $12 to make that is $6900
\n" ); document.write( "Subtracting that from the maximum revenue leaves a profit of $12366.67
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\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "