document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=389358>Question 389358</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My question was already answered by Charles I think and he did an awesome job but he didn't tell me what the variables were so now i can't figure it out! Here's the question. If you can somewhat explain it, that'd be great. <BR>\n" );
document.write( "A company makes two products, televisions and DVD players. The televisions require two hours of labor and $100 of materials per television. The profit per television is $300. The DVD player requires three hours of labor and $50 of materials per DVD player. The profit per player is $150. The company can afford to spend $1000 each week for the cost of the material. If an employee works forty hours a week, how many televisions and/or DVD players should the employee make in order to maximize the company's profit?<BR>\n" );
document.write( "Thanks in advance! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #275943 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=275943\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"My question was already answered by Charles I think and he did an awesome job but he didn't tell me what the variables were so now i can't figure it out! Here's the question. If you can somewhat explain it, that'd be great. <BR>\n" );
document.write( "A company makes two products, televisions and DVD players. The televisions require two hours of labor and $100 of materials per television. The profit per television is $300. The DVD player requires three hours of labor and $50 of materials per DVD player. The profit per player is $150. The company can afford to spend $1000 each week for the cost of the material. If an employee works forty hours a week, how many televisions and/or DVD players should the employee make in order to maximize the company's profit?<BR>\n" );
document.write( "Thanks in advance!\"\r<BR>\n" );
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document.write( "A company makes two products, televisions and DVD players. The televisions require two hours of labor and $100 of materials per television. The profit per television is $300. The DVD player requires three hours of labor and $50 of materials per DVD player. The profit per player is $150. The company can afford to spend $1000 each week for the cost of the material. If an employee works forty hours a week, how many televisions and/or DVD players should the employee make in order to maximize the company's profit? \r<BR>\n" );
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document.write( "number of televisions (T) * materials/televison (100) + number of DVD players (D) * materials/DVD player (50) = $1000 per week --> 100T + 50D = 1000<BR>\n" );
document.write( "number of televisions (T) * hours/television (2) + number of DVD players (D) * hours/DVD player (3) = 40 hours --> 2T + 3D = 40<BR>\n" );
document.write( "number of televisions (T) * profit/television (300) + number of DVD players (D) * profit/DVD player (150) = total profit per week --> 300T + 150D<BR>\n" );
document.write( "number of televisions (T) * sales price/televison + number of DVD players (D) * sales price/DVD player = total sales in a week\r<BR>\n" );
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document.write( "profit = sales - costs <BR>\n" );
document.write( "costs + profit = sales (this equation rearranging of above equation)<BR>\n" );
document.write( "costs = sales - profit (also rearranging of above equation)\r<BR>\n" );
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document.write( "let W = employee's wage/hr<BR>\n" );
document.write( "television --> 2 * wage/hr + 100 + 300 = 2W + 400 --> sales price per television<BR>\n" );
document.write( "DVD ---------> 3 * wage/hr + 50 + 150 = 3W + 200 --> sales price per DVD player\r<BR>\n" );
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document.write( "let T = televisions, let D = DVD players\r<BR>\n" );
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document.write( "100T + 50D = 1000 (total materials cost)<BR>\n" );
document.write( "2T + 3D = 40 (total hours) --> \r<BR>\n" );
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document.write( "T = (40 - 3D)/2 --> substitute into 100T + 50D = 1000<BR>\n" );
document.write( "100 * (40 - 3D)/2 + 50D = 1000<BR>\n" );
document.write( "50 * (40 - 3D) + 50D = 1000 (above line simplified)<BR>\n" );
document.write( "2000 - 150D + 50D = 1000 (distributed the 50)<BR>\n" );
document.write( "2000 - 100D = 1000 (above line simplified)<BR>\n" );
document.write( "-100D = -1000<BR>\n" );
document.write( "100D = 1000<BR>\n" );
document.write( "D = 10 DVD players\r<BR>\n" );
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document.write( "2T + 3D = 40 --> 2T + 30 = 40 (plugged in 10 for D)<BR>\n" );
document.write( "2T = 10<BR>\n" );
document.write( "T = 5 televisions\r<BR>\n" );
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document.write( "materials: 100T + 50D = 1000 --> 500 + 500 = 1000 (plugged in values for D and T)\r<BR>\n" );
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document.write( "5 televisions, and 10 dvd's\r<BR>\n" );
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document.write( "5 * (2W + 400) + 10 * (3W + 200) (plugged in sales prices)<BR>\n" );
document.write( "10W + 2000 + 30W + 2000\r<BR>\n" );
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document.write( "40W + 4000 --> total sales in a week\r<BR>\n" );
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document.write( "total profit in a week: 300T + 150D = 5 * 300 + 10 * 150 = 1500 + 1500 = $3000\r<BR>\n" );
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document.write( "costs to make television plus pay employee = 40W + 4000 - 3000 = 40W + 1000\r<BR>\n" );
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document.write( "Hope this helps\r<BR>\n" );
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