document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192502>Question 1192502</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A baking company sells cakes by weight. The demand for cakes, on a day varies in a <BR>\n" );
document.write( "uniform manner between 2000 kgs and 3000 kgs. Further, he finds the distribution of profit as given below\r<BR>\n" );
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document.write( "Daily demand(in Kgs) -- Average profit\r<BR>\n" );
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document.write( "2000-2250 -- 981.5<BR>\n" );
document.write( "2250-2500 -- 1136.5<BR>\n" );
document.write( "2500-3000 -- 1344.2\r<BR>\n" );
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document.write( "Calculate the probability that on a randomly selected day the demand lies between <BR>\n" );
document.write( "(i) 2000-2250 kgs, (ii) 2250- 2500 kgs (iii) 2500- 3000 kgs, hence obtaining the expected profit on a randomly chosen day </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848979 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848979\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Calculate the Probability of Each Demand Range**\r<BR>\n" );
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document.write( "* **Total Range of Demand:** 3000 kgs - 2000 kgs = 1000 kgs\r<BR>\n" );
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document.write( "* **Probability of Demand between 2000-2250 kgs:** <BR>\n" );
document.write( "   (2250 kgs - 2000 kgs) / 1000 kgs = 250 kgs / 1000 kgs = 0.25\r<BR>\n" );
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document.write( "* **Probability of Demand between 2250-2500 kgs:** <BR>\n" );
document.write( "   (2500 kgs - 2250 kgs) / 1000 kgs = 250 kgs / 1000 kgs = 0.25\r<BR>\n" );
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document.write( "* **Probability of Demand between 2500-3000 kgs:** <BR>\n" );
document.write( "   (3000 kgs - 2500 kgs) / 1000 kgs = 500 kgs / 1000 kgs = 0.50\r<BR>\n" );
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document.write( "**2. Calculate the Expected Profit**\r<BR>\n" );
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document.write( "* **Expected Profit:** <BR>\n" );
document.write( "   (Probability of Range 1 * Average Profit of Range 1) + <BR>\n" );
document.write( "   (Probability of Range 2 * Average Profit of Range 2) + <BR>\n" );
document.write( "   (Probability of Range 3 * Average Profit of Range 3)\r<BR>\n" );
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document.write( "   = (0.25 * 981.5) + (0.25 * 1136.5) + (0.50 * 1344.2) <BR>\n" );
document.write( "   = 245.375 + 284.125 + 672.1 <BR>\n" );
document.write( "   = **1201.6**\r<BR>\n" );
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document.write( "**Therefore:**\r<BR>\n" );
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document.write( "* The probability of demand between 2000-2250 kgs is 0.25.<BR>\n" );
document.write( "* The probability of demand between 2250-2500 kgs is 0.25.<BR>\n" );
document.write( "* The probability of demand between 2500-3000 kgs is 0.50.<BR>\n" );
document.write( "* The expected profit on a randomly chosen day is $1201.60.<BR>\n" );
document.write( " </SPAN>\n" );
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