document.write( "Question 1199213: A candy manufacturer makes two types of special candy, say A and B. Candy A consists of equal
\n" ); document.write( "part of dark chocolate and caramel and Candy B consists of two parts of dark chocolate and one\r
\n" ); document.write( "\n" ); document.write( "part of walnut. The company has in stock 430 kilograms of caramel, 360 kilograms of dark\r
\n" ); document.write( "\n" ); document.write( "chocolate, and 210 kilograms of walnuts. The company sells Candy A for P285 and Candy B for\r
\n" ); document.write( "\n" ); document.write( "P260 per kilograms. How much of each candy should the manufacturer produce to maximize profit? \n" ); document.write( "

Algebra.Com's Answer #832999 by ikleyn(52794) $\"\"$ $\"About$

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\n" ); document.write( "A candy manufacturer makes two types of special candy, say A and B. Candy A consists of equal
\n" ); document.write( "part of dark chocolate and caramel and Candy B consists of two parts of dark chocolate and one
\n" ); document.write( "part of walnut. The company has in stock 430 kilograms of caramel, 360 kilograms of dark
\n" ); document.write( "chocolate, and 210 kilograms of walnuts. The company sells Candy A for P285 and Candy B for
\n" ); document.write( "P260 per kilograms. How much of each candy should the manufacturer produce to maximize profit?
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document.write( "Let x = kilograms of Candy A,\r\n" );
document.write( "    y = kilograms of Candy B.\r\n" );
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document.write( "Then A uses   kg of dark chocolate and   kg of caramel;\r\n" );
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document.write( "     B uses   kg of dark chocolate and   kg of walnut.\r\n" );
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document.write( "The restrictions from the problem are\r\n" );
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document.write( "     <= 430                  (1)  (caramel)\r\n" );
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document.write( "     +  <= 360          (2)  (dark chocolate)\r\n" );
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document.write( "     <= 210                  (3)  (walnut)\r\n" );
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document.write( "    x >= 0, y >= 0             (4)  (non-negativity)\r\n" );
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document.write( "The profit function is  P(x,y) = 285x + 260y.\r\n" );
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document.write( "By riding from the denominators in (1), (2) and (3), we get the standard form of the linear minimax problem\r\n" );
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document.write( "    \r\n" );
document.write( "Maximize p = 285x + 260y subject to\r\n" );
document.write( "x <= 860 \r\n" );
document.write( "3x + 4y <= 2160\r\n" );
document.write( "y <= 630\r\n" );
document.write( "x >= 0  \r\n" );
document.write( "y >= 0\r\n" );
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document.write( "Now go to web-site https://www.zweigmedia.com/RealWorld/simplex.html\r\n" );
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document.write( "and use free of charge online solver specially intended for such Linear Programming problems.\r\n" );
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document.write( "Copy-paste this standard input above to the input window port of the solver and click the button \"Solve\".\r\n" );
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document.write( "You will get the answer  x = 720, y = 0, p = 205200.\r\n" );
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document.write( "So, the optimal strategy is to produce and to cell 720 kg of candy A only \r\n" );
document.write( "and do not produce candy B, at all.\r\n" );
document.write( "It gives the maximum profit of Php 205200.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "In the post by @shin123, the reasoning for deriving the constraints is incorrect, and his constraints are incorrect, too,\r
\n" ); document.write( "\n" ); document.write( "although the final answer is correct and coincides with my answer.\r
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\n" ); document.write( "\n" ); document.write( "In this problem, the major interest is to create a correct setup, so I concentrated on it.
\n" ); document.write( "Making a correct setup was my primary goal.\r
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\n" ); document.write( "\n" ); document.write( "The technique of solving plays a subordinate role in this problem,
\n" ); document.write( "so and therefore, I used the automatic online solver (software) to save my time.\r
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\n" ); document.write( "\n" ); document.write( "The problem also can be solved mentally, based on common sense.\r
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\n" ); document.write( "\n" ); document.write( "Indeed, it is clear that the constraint for walnut does not work, actually: it is not a working constraint:
\n" ); document.write( "there are enough walnut for any purposes.\r
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\n" ); document.write( "\n" ); document.write( "Next, looking on the input numbers, it is clear, that it is more profitable to make candy A only and to use full amount
\n" ); document.write( "of the chocolate for this purpose, since candy A bring more profit and resources allow to use the chocolate in full.\r
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\n" ); document.write( "\n" ); document.write( "The only working constrain in this problem is the dark chocolate constrain (2).\r
\n" ); document.write( "\n" ); document.write( "It controls (governs) the entire problem.\r
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