document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195573>Question 1195573</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can I please have help with this, Thank you!<BR>\n" );
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document.write( "Sharon has applied to the navy. She plans to racquetball and cycle to get into shape for the fitness test. Sharon wants to spend no more than 12 hours exercising a week and wants to burn a maximum of 7000 calories. She ahs calculated she will burn 700 calories per hour playing racquetball and 350 calories per hour cycling.\r<BR>\n" );
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document.write( "To describe this scenario, what quantities should x and y represent\r<BR>\n" );
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document.write( "     B.  Write a system of inequalities which will represent Sharon’s situation( Hint: three are 4 linear inequalities for this scenario)\r<BR>\n" );
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document.write( "C. Graph the system of inequalities, mark the points of intersection of all lines and shade the solution region.\r<BR>\n" );
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document.write( "D. Bicycling is free but racquetball costs $20 per hour to play. Write the objective function for this scenario. How much time should she spend on each activity in orde to minimize costs?\r<BR>\n" );
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document.write( "E. How much time should she spend on each activity if she just wants to maximize her calorie burn? \r<BR>\n" );
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document.write( "The diagram has the line 4x+3y=12 dividing the Cartesian Plane into seven regions. Write a system of inequalities the describes region D.<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 #828115 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=828115\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the number of hours playing racquetball.<BR>\n" );
document.write( "let y = the number of hours cycling.<BR>\n" );
document.write( "your inequalities are:<BR>\n" );
document.write( "x + y <= 12<BR>\n" );
document.write( "this represents the total number of hours she wants to use is less than 12.<BR>\n" );
document.write( "700x + 350y <= 7000<BR>\n" );
document.write( "this represents the total number of calories she wants to burn.<BR>\n" );
document.write( "it's 700 calories per hour times the number of hours for racquetball plus 350 calories per hour times the number of hours for cycling.<BR>\n" );
document.write( "x >= 0<BR>\n" );
document.write( "y >= 0<BR>\n" );
document.write( "this represents that the number of hours for each activity can't be less than 0.<BR>\n" );
document.write( "if she wants to minimize costs, then the objective function for costs is:<BR>\n" );
document.write( "20x + 0y, which you want to minimize.<BR>\n" );
document.write( "this represents 20 dollars per hour for racquetball plus 0 dollars for cycling.<BR>\n" );
document.write( "if she wants maximize calories consumed, then the objective function for calories is:<BR>\n" );
document.write( "700x + 350y, which you want to maximize.<BR>\n" );
document.write( "this represents 700 calories per hour times number of hours for racquetball plus 350 calories per hour times number of hours for cycling.<BR>\n" );
document.write( "you can graph this manually, or you can use the calculator at desmos.com.<BR>\n" );
document.write( "if you use the calculator at desmos.com, you would:<BR>\n" );
document.write( "graph the opposite of the inequalities.<BR>\n" );
document.write( "the area of the graph that is not shaded will be your region of feasibility.<BR>\n" );
document.write( "the corner points of the region of feasibility will be where your maximum calory burn and your minimum cost will be.<BR>\n" );
document.write( "objective function for cost is 20x + 0y<BR>\n" );
document.write( "objective function for calories is 700x + 350y<BR>\n" );
document.write( "constraint inequalities are:<BR>\n" );
document.write( "x + y <= 12<BR>\n" );
document.write( "700x + 350y <= 7000<BR>\n" );
document.write( "x >= 0<BR>\n" );
document.write( "y >= 0<BR>\n" );
document.write( "graph  the opposite of the inequalities.<BR>\n" );
document.write( "identify the corner points.<BR>\n" );
document.write( "evaluate the objective functions at the corner points.<BR>\n" );
document.write( "the graph looks like this.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/072102.jpg\"><BR>\n" );
document.write( "the corner points of the feasible region are:<BR>\n" );
document.write( "(0,12)<BR>\n" );
document.write( "(8,4)<BR>\n" );
document.write( "(10,0)<BR>\n" );
document.write( "the minimum cost will be at (0,12), where the cost is 20 * 0 + 0 * 12 = 0.<BR>\n" );
document.write( "the maximum calorie burn will be at (10,0) or (8,4).<BR>\n" );
document.write( "at (10,0), the maximum calorie burn is 10 * 700 = 7000<BR>\n" );
document.write( "at (8,4), the maximum calories burn is 8 * 700 + 4 * 350 = 7000.<BR>\n" );
document.write( "you have a minimum cost of 0 and a maximum calorie burn of 7000.<BR>\n" );
document.write( "i have no idea what the equation of 4x + 3y = 12 represents.<BR>\n" );
document.write( "i don't see it as being applicable to this problem, unless there is some other information about the problem that you didn't show.<BR>\n" );
document.write( "if you were to manually create the graph, you would do the following.<BR>\n" );
document.write( "graph the equations of:<BR>\n" );
document.write( "x + y = 12<BR>\n" );
document.write( "700x + 350y = 7000<BR>\n" );
document.write( "x = 0<BR>\n" );
document.write( "y = 0<BR>\n" );
document.write( "you would then shade the areas for the inequalities of:<BR>\n" );
document.write( "x + y <= 12<BR>\n" );
document.write( "700x + 3506 <= 7000<BR>\n" );
document.write( "x >= 0<BR>\n" );
document.write( "y >= 0<BR>\n" );
document.write( "that graph would look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/072103.jpg\" ><BR>\n" );
document.write( "using desmos.com calculator, the region of feasibility is the area that is  not shaded.<BR>\n" );
document.write( "doing it manually, the region of feasibility is the area that is shaded.<BR>\n" );
document.write( "the region of feasibility is the same, whichever way you wanted to graph it.<BR>\n" );
document.write( "the corner points are the same and the analysis is the same.<BR>\n" );
document.write( "note that, when she minimizes cost, the maximum calorie burn is 12 * 350 = 4200.<BR>\n" );
document.write( "this is acceptable since it is less than 7000, which was one of the constraints.<BR>\n" );
document.write( "all of the constraints need to be satisfied, not just some of them.<BR>\n" );
document.write( "at (0,12), she had exercised for 12 hours which is <= 12 and she had burned 4200 calories which is <= 7000.<BR>\n" );
document.write( "at (8,4), she had exercised for 12 hours which is <= 12 and she had burned 7000 calories which is <= 7000.<BR>\n" );
document.write( "at (10,0), she had exercised for 12 hours which is <= 12 and she had burned 7000 calories which is <= 7000.<BR>\n" );
document.write( "let me know if you have any questions.<BR>\n" );
document.write( "theo </SPAN>\n" );
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