document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155260>Question 1155260</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A manufacturing firm has 120 hours per week available in one of its department. Two products are produced through this department. <BR>\n" );
document.write( "Product A requires 4 hours per unit and product B requires 6 hours per unit in this department. <BR>\n" );
document.write( "If x equals the number of units of product A per week and y equals the number of  units of products B produced per week.<BR>\n" );
document.write( "a) Determine the equation which states the total time expended for producing these two products equals 120 hours per week<BR>\n" );
document.write( "b) Rewrite the equation in the slope intercept from and identify the slope and y intercept<BR>\n" );
document.write( "c) Interpret the meaning of the slope and y intercept in this application.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #777840 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=777840\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = number of units of product A per week.<BR>\n" );
document.write( "y = number of units of product B per week.<BR>\n" );
document.write( "product A requires 4 hours per unit and product B requires 6 hours per unit.<BR>\n" );
document.write( "total hours available per week = 120.<BR>\n" );
document.write( "equation becomes 4x + 6y = 120<BR>\n" );
document.write( "convert this to slope intercept form as follows:<BR>\n" );
document.write( "subtract 4x from both sides of the equation and arrange the right side of the equation in descending order of degree to get:<BR>\n" );
document.write( "6y = -4x + 120<BR>\n" );
document.write( "divide both sides of this equation by 6 to get:<BR>\n" );
document.write( "y = -4/6 * x + 120 / 6<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "y = -2/3 * x + 20<BR>\n" );
document.write( "questions to answer are:\r<BR>\n" );
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document.write( "a) Determine the equation which states the total time expended for producing these two products equals 120 hours per week\r<BR>\n" );
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document.write( "4x + 6y = 120\r<BR>\n" );
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document.write( "this equation says that 4 hours are expended for every unit of product A and 6 hours are expended for every unit of product B.<BR>\n" );
document.write( "x = the number of units for product A.<BR>\n" );
document.write( "y = the number of units for product B.\r<BR>\n" );
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document.write( "b) Rewrite the equation in the slope intercept from and identify the slope and y intercept\r<BR>\n" );
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document.write( "y = -2/3 * x + 20\r<BR>\n" );
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document.write( "the general form of the slope intercept form of the equation is y = mx + b<BR>\n" );
document.write( "m is the slope and b is the y-intercept.<BR>\n" );
document.write( "m = -2/3<BR>\n" );
document.write( "y-intercept = 20\r<BR>\n" );
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document.write( "c) Interpret the meaning of the slope and y intercept in this application. \r<BR>\n" );
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document.write( "the y-intercept is the value of y when x = 0.<BR>\n" );
document.write( "when x = 0, the formula becomes y = 20.<BR>\n" );
document.write( "this is saying that, if no units of product A are produced, and 120 hours a week are still required, than 20 units of product B are produced.\r<BR>\n" );
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document.write( "the slope tells you the change in the number of units of y for every change in the number of units for x.<BR>\n" );
document.write( "a slope of -2/3 is equivalent to (-2/3) / 1.<BR>\n" );
document.write( "this says that, when x increases by 1, y decreases by 2/3.<BR>\n" );
document.write( "this translates to the change in the number of units of product B for every change in the number of units of product A.<BR>\n" );
document.write( "it says that, when the number of units of product A increases by 1, the number of units of product B decreases by 2/3.\r<BR>\n" );
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document.write( "it might be useful to show you what happens via a graph.<BR>\n" );
document.write( "the graph is shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/040401.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "you can see that, when x = 0, y = 20.<BR>\n" );
document.write( "this means that no units are produced for product A and 20 units are produced for product B.\r<BR>\n" );
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document.write( "you can see that, when x = 6, y = 16 and when x = 12, y = 12.\r<BR>\n" );
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document.write( "y = -2/3 * x + 20 is the equation.<BR>\n" );
document.write( "when x = 6, y = -2/3 * 6 + 20 which becomes y = -4 + 20 which becomes y = 16.<BR>\n" );
document.write( "when x = 12, y = -2/3 * 12 + 20 which becomes y = -8 + 20 which becomes y = 12.\r<BR>\n" );
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document.write( "the change in x from 6 to 12 is 6.<BR>\n" );
document.write( "the change in y from 16 to 12 is -4.<BR>\n" );
document.write( "the change in y divided by the change in x is -4/6 which simplifies to -2/3.<BR>\n" );
document.write( "that's your slope.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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