document.write( "Question 1176024: Evan runs a factory that makes Blu-ray players. Each T50 takes 4 ounces of plastic and 4 ounces of metal. Each G150 requires 2 ounces of plastic and 6 ounces of metal. The factory has 140 ounces of plastic, 324 ounces of metal available, with a maximum of 16 T50 that can be built each week. If each T50 generates $12 in profit, and each G150 generates $11, how many of each of the Blu-ray players should Evan have the factory make each week to make the most profit?\r
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Algebra.Com's Answer #801934 by ikleyn(52906) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Evan runs a factory that makes Blu-ray players. Each T50 takes 4 ounces of plastic and 4 ounces of metal.
\n" ); document.write( "Each G150 requires 2 ounces of plastic and 6 ounces of metal.
\n" ); document.write( "The factory has 140 ounces of plastic, 324 ounces of metal available, with a maximum of 16 T50 that can be built each week.
\n" ); document.write( "If each T50 generates $12 in profit, and each G150 generates $11, how many of each of the Blu-ray players should
\n" ); document.write( "Evan have the factory make each week to make the most profit?
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document.write( "Let X = # of items T50;  Y = # of items G150.\r\n" );
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document.write( "From the condition, we have this formulation of maximization problem:\r\n" );
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document.write( "    (1)  the objective function to maximize is the profit  P = 12X + 11Y  dollars.\r\n" );
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document.write( "Restrictions\r\n" );
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document.write( "    (2)  4X + 2Y <=  140            (plastic restriction)\r\n" );
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document.write( "    (3)  4X + 6Y <=  324            (metal restriction)\r\n" );
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document.write( "    (4)   0 <= X <= 16,  Y >= 0.\r\n" );
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document.write( "You can make a plot of the feasibility domain.\r\n" );
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document.write( "    \r\n" );
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document.write( "    Plots y =   (red);  y =  (green);  x = 16 (blue)\r\n" );
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document.write( "It is a pentagon in QI adjacent to x- and y-axes, restricted by the red, the green and the blue lines.\r\n" );
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document.write( "It has vertices (X,Y) = (0,0), (0,54), (12,46), (16,38), (16,0).\r\n" );
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document.write( "The solution is one of these 5 points, where the objective function (profit) has a maximum.\r\n" );
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document.write( "The values of the function  P(X,Y)  at listed points are\r\n" );
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document.write( "    P(0,0)                      =   0,\r\n" );
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document.write( "    P(0,54)   = 12*0  + 11*54   = 594,\r\n" );
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document.write( "    P(12,46)  = 12*12 + 11*46   = 650,\r\n" );
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document.write( "    P(16,38)  = 12*16 + 11*38   = 610,\r\n" );
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document.write( "    P(16,0)   = 12*16  + 11*0   = 192.\r\n" );
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document.write( "Comparing these values, you find the optimal point.\r\n" );
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document.write( "It is  (X,Y) = (12,46),  12 items T50 and 46 items G150, providing maximum profit of 650 dollars.     ANSWER\r\n" );
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