document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196009>Question 1196009</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Refer to the graphs. Assume that pizza is measured in slices and beer in pints. In which of the graphs is the opportunity cost of a pint of beer the lowest? There are four graphs. Graph A has points (0,8) and (5, 0). Graph B has points (0, 5) and (8,0), graph C has points (0, 1.25) and (2.00, 0), and graph d (0, 10) and (10,0). The \"x\" axis represents beer and the \"y\" axis represents pizza.\r<BR>\n" );
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document.write( "My work: I tried to add extra points on the graph to figure it out. Then I tried to compare the graphs and select a graph where there wasn't a wide distrance between the points on the x axis and y axis. </SPAN>\n" );
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document.write( "The graphs aren't shown. There's missing info.\r<BR>\n" );
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document.write( "For this problem I'll assume that each graph is linear. <BR>\n" );
document.write( "If the assumption is incorrect, then please let me know so I can fix things.\r<BR>\n" );
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document.write( "x = amount of beer in pints<BR>\n" );
document.write( "y = amount of pizza in number of slices<BR>\n" );
document.write( "A point like (x,y) = (0,8) means x = 0 and y = 8 pair up together<BR>\n" );
document.write( "We have 0 pints of beer and 8 slices of pizza.\r<BR>\n" );
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document.write( "Graph A goes through (0,8) and (5,0)<BR>\n" );
document.write( "Compute the slope<BR>\n" );
document.write( "m = slope<BR>\n" );
document.write( "m = rise/run<BR>\n" );
document.write( "m = (change in y)/(change in x)<BR>\n" );
document.write( "m = (y2 - y1)/(x2 - x1)<BR>\n" );
document.write( "m = (0-8)/(5-0)<BR>\n" );
document.write( "m = -8/5<BR>\n" );
document.write( "m = -1.6<BR>\n" );
document.write( "The slope is m = -1.6\r<BR>\n" );
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document.write( "This tells us that each time x goes up by 1, then y goes down by 1.6<BR>\n" );
document.write( "It means each time you buy a pint of beer, the number of slices you buy goes down by 1.6 slices.<BR>\n" );
document.write( "In other words, for each pint of beer, you give up 1.6 slices of pizza.\r<BR>\n" );
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document.write( "We want to flip things so that we find out how much beer we give up for each extra slice purchased.<BR>\n" );
document.write( "This means we'll need the reciprocal, which conveniently enough flips the fraction.\r<BR>\n" );
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document.write( "Apply the reciprocal<BR>\n" );
document.write( "-8/5 flips to -5/8 = -0.625<BR>\n" );
document.write( "Doing this let's us see that each time y goes up by 1, x will drop by 0.625<BR>\n" );
document.write( "For each slice of pizza you get, you give up the chance of buying 0.625 pints of beer. <BR>\n" );
document.write( "This is the opportunity cost for the beer in graph A.\r<BR>\n" );
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document.write( "Compute the slope of graph B<BR>\n" );
document.write( "m = rise/run<BR>\n" );
document.write( "m = (change in y)/(change in x)<BR>\n" );
document.write( "m = (y2 - y1)/(x2 - x1)<BR>\n" );
document.write( "m = (0-5)/(8-0)<BR>\n" );
document.write( "m = -5/8<BR>\n" );
document.write( "m = -0.625<BR>\n" );
document.write( "Then apply the reciprocal<BR>\n" );
document.write( "-5/8 flips to -8/5 = -1.6<BR>\n" );
document.write( "For each slice of pizza you get, you give up 1.6 pints of beer. This result (1.6) is larger than the previous result (0.625)<BR>\n" );
document.write( "Therefore graph A has the lowest opportunity cost so far.\r<BR>\n" );
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document.write( "Now find the slope of graph C<BR>\n" );
document.write( "m = rise/run<BR>\n" );
document.write( "m = (change in y)/(change in x)<BR>\n" );
document.write( "m = (y2 - y1)/(x2 - x1)<BR>\n" );
document.write( "m = (0-1.25)/(2-0)<BR>\n" );
document.write( "m = -1.25/2<BR>\n" );
document.write( "m = -0.625<BR>\n" );
document.write( "m = -5/8<BR>\n" );
document.write( "This flips to -8/5 = -1.6<BR>\n" );
document.write( "We get the same opportunity cost as graph B.\r<BR>\n" );
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document.write( "Lastly compute the slope of graph D<BR>\n" );
document.write( "m = slope<BR>\n" );
document.write( "m = rise/run<BR>\n" );
document.write( "m = (change in y)/(change in x)<BR>\n" );
document.write( "m = (y2 - y1)/(x2 - x1)<BR>\n" );
document.write( "m = (0-10)/(10-0)<BR>\n" );
document.write( "m = -10/10<BR>\n" );
document.write( "m = -1<BR>\n" );
document.write( "The reciprocal of this is -1/1 or simply -1<BR>\n" );
document.write( "Nothing changes.<BR>\n" );
document.write( "For each slice of pizza you get, you give up 1 pint of beer.<BR>\n" );
document.write( "This opportunity cost (1) is not smaller than graph A's opportunity cost (0.625)\r<BR>\n" );
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document.write( "Here is a summary of the opportunity costs of beer for each graph<BR>\n" );
document.write( "<ul><li>A) 0.625</li><li>B) 1.6</li><li>C) 1.6</li><li>D) 1</li></ul>\r<BR>\n" );
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document.write( "Answer: <font color=red>Graph A</font> has the lowest opportunity cost for the pints of beer.<BR>\n" );
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