document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138881>Question 1138881</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A consumer has income of $3,000. Juice costs $3 per glass, and cheese costs $6 per pound. Draw the consumer’s budget constraint with juice on the vertical axis. What is the slope of this budget constraint? *<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #756660 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=756660\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> income is 3000.<BR>\n" );
document.write( "juice costs 3 per glass.<BR>\n" );
document.write( "cheese costs 6 per pound.\r<BR>\n" );
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document.write( "let x = the number of pounds of cheese.<BR>\n" );
document.write( "let y = the number of glasses of juice.\r<BR>\n" );
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document.write( "if that is all that is being bought is 3000, then the inequality becomes:\r<BR>\n" );
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document.write( "6x + 3y <= 3000\r<BR>\n" );
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document.write( "subtract 6x from both sides of this inequality to get 3y <= 3000 - 6x.<BR>\n" );
document.write( "divide both sides of this inequality by 6 to get y <= 1000 - 2x.<BR>\n" );
document.write( "arrange the terms in descending order of degree to get y <= -2x + 1000.\r<BR>\n" );
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document.write( "6x + 3y <= 3000 is your inequality in standard form.<BR>\n" );
document.write( "y <= -2x + 1000 is your inequality in slope intercept form.\r<BR>\n" );
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document.write( "the slope of the inequality is -2.<BR>\n" );
document.write( "the y-intercept of the inequality is 1000.\r<BR>\n" );
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document.write( "that can be seen easily by looking at the slope intercept form of the inequality.\r<BR>\n" );
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document.write( "the slope intercept form of your inequality is y <= mx + b\r<BR>\n" );
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document.write( "m is the slope<BR>\n" );
document.write( "b is the y-intercept.\r<BR>\n" );
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document.write( "since the ineqquality is y <= -2x + 1000, .....<BR>\n" );
document.write( "the slope is -2.<BR>\n" );
document.write( "the y-intercept is 1000.\r<BR>\n" );
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document.write( "the graph of your inequality looks like this.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/041121.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the number of pounds of cheese are measured on the x-axis.<BR>\n" );
document.write( "the number of glasses of juice are measured on the y-axis.\r<BR>\n" );
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document.write( "when x = 100, the range of y is between 0 and 800.<BR>\n" );
document.write( "when y = 500, the range of x is between 0 and 250.\r<BR>\n" );
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document.write( "for example, as shown on the graph.\r<BR>\n" );
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document.write( "when y = 500, the maximum value of x is 250.<BR>\n" );
document.write( "that buys 250 pounds of cheese and 500 glasses of juice.<BR>\n" );
document.write( "total cost is 6 * 250 + 3 * 500 = 3000 dollars.\r<BR>\n" );
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document.write( "when x = 100, the maximum value of y is 800.<BR>\n" );
document.write( "that buys 100 pounds of cheese and 800 glasses of juice.<BR>\n" );
document.write( "total cost is 6 * 100 + 3 * 800 = 3000 dollars.\r<BR>\n" );
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document.write( "when y = 500, any value of x between 0 and 250 is valid.<BR>\n" );
document.write( "when x = 100, any value of y between 0 and 800 is valid.\r<BR>\n" );
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document.write( "since this is an inequality, any value on the graph that is not shaded will give you a valid value for (x,y) coordinate pairs.\r<BR>\n" );
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document.write( "for example, when x = 100 and y = 500, you would be buying 100 pounds of cheese and 500 glasses of orange juice for a total cost of 6 * 100 + 3 * 500 = 2100.\r<BR>\n" );
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document.write( "since you paid less than 3000, the inequality holds true.\r<BR>\n" );
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document.write( "you were asked for the slope of this budget constraint.\r<BR>\n" );
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document.write( "the slope is -2.\r<BR>\n" );
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document.write( "note that i graphed the opposite of the inequality.\r<BR>\n" );
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document.write( "this allows me to see the region of feasibility easier because that becomes the un-shaded part of the graph rather than the shaded part of the graph.\r<BR>\n" );
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document.write( "not all graphing calculators allows you to show inequalities or to show linear equations in the form of ax + by = c.   \r<BR>\n" );
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document.write( "the desmos.com calculator allows this which makes graphing inequalities much easier and automatically generated.\r<BR>\n" );
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