document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1062038>Question 1062038</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Good evening, can you please help me solve the 3rd one? Thank you very much!\r<BR>\n" );
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document.write( "(1) An office manager needs to staff the office. She hires full-time employees at $18 per our and part-time employees at $12 per hour. Write an objective function that represents the total cost (in $) to staff the office with x full-time employees and y part-time employees for 1 hr.<BR>\n" );
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document.write( "ANSWER: Total cost: z = 18x + 12y<BR>\n" );
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document.write( "(2) Refer to 1. Suppose that the office manager needs at least 20 employees, but not more than 24 full-time employees. Furthermore, to make the office run smoothly, the manager knows that the number of full-time employees must always be greater than or equal to the number of part-time employees. Write a system of inequalities that represents the constraints on the number of full-time employees x and the number of part-time employees y.<BR>\n" );
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document.write( "ANSWER:  x+y&#8805;20<BR>\n" );
document.write( "                x&#8804;24<BR>\n" );
document.write( "                x&#8805;y<BR>\n" );
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document.write( "(3) Refer to no's 1 and 2. The office manager needs at least 20 employees, but not more than 24 full-time employees. Furthermore, to make the office run smoothly, the manager knows that the number of full-time employees must always be greater than or equal to the number of part-time employees. If she pays full-time employees $18 per hour and part-time employees $12 per hour, determine the number of full-time and part-time employees she should hire to minimize total labor cost per hour. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #676799 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52797)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=676799\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "(2) You should amplify your inequalities in the n(2) with these two inequalities: x >= 0,   y >= 0.\r\n" );
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document.write( "    (as I said in my preceding post).\r\n" );
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document.write( "(3) Your area to apply the linear programming method is shown in the figure below:\r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-3.5%2C+30.5%2C+-3.5%2C+30.5%2C%0D%0A++++++++++++grid%281%29%2C%0D%0A++++++++++++line+%280%2C+20%2C+20%2C+0%29%2C%0D%0A++++++++red%28line+%2824%2C+0%2C+24%2C+30%29%29%2C%0D%0A+++++++blue%28line+%280%2C++0%2C+30%2C+30%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( "Lines  x + y >= 20 (black),  x = 24 (red),  y = x (blue)\r\n" );
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document.write( "This area is the quadrilateral in the first quadrant, restricted by the straight line x+y >= 20 (black), <BR>\n" );
document.write( "straight line  y = x  (blue), vertical line x = 24 (red) and horizontal line y = 0.\r<BR>\n" );
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document.write( "According to the linear programming method, you should calculate your objective function in four vertices of the quadrilateral <BR>\n" );
document.write( "and choose the point where the objective function is minimal.\r<BR>\n" );
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document.write( "This point is your solution.<BR>\n" );
document.write( "Together with the minimal value of the objective function.\r<BR>\n" );
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document.write( "That's all.\r<BR>\n" );
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