document.write( "Question 84975: A linear programming feasible region is determined by\r
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\n" ); document.write( "\n" ); document.write( "6x + 3y (is less or equal to) 72
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\n" ); document.write( "\n" ); document.write( "Which of the follwoing objective functions has its maximum value at the intersection of\r
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\n" ); document.write( "\n" ); document.write( "6x + 3y = 72 and
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\n" ); document.write( "\n" ); document.write( "A. Z = 10x + 10y
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Algebra.Com's Answer #61227 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "A linear programming feasible region is determined by\r\n" );
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document.write( "6x + 3y < 72\r\n" );
document.write( "5x + 15y < 185\r\n" );
document.write( "x > 0, y > 0 \r\n" );
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document.write( "Which of the following objective functions has\r\n" );
document.write( "its maximum value at the intersection of \r\n" );
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document.write( "6x + 3y = 72 and\r\n" );
document.write( "5x + 15y = 185 \r\n" );
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document.write( "A. Z = 10x + 10y\r\n" );
document.write( "B. Z = 5x + 2y\r\n" );
document.write( "C. Z = 2x + 8y\r\n" );
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document.write( "Graph the four boundary lines:\r\n" );
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document.write( "6x + 3y = 72  (6x + 3y < 72 will \r\n" );
document.write( "be the region on or below this line)\r\n" );
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document.write( "5x + 15y = 185  (5x + 15y < 185 \r\n" );
document.write( "will be the region on or below this\r\n" );
document.write( "line.\r\n" );
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document.write( "x = 0  (this is the y-axis, x > 0 \r\n" );
document.write( "will be the region to the right of the\r\n" );
document.write( "y-axis.\r\n" );
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document.write( "y = 0  (this is the x-axis, y > 0 \r\n" );
document.write( "will be the region above the x-axis.\r\n" );
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document.write( "You must solve this system \r\n" );
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document.write( "6x +  3y = 72 \r\n" );
document.write( "5x + 15y = 185 \r\n" );
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document.write( "To find out where the lines intersect:\r\n" );
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document.write( "I assume you can do this, the intersection\r\n" );
document.write( "is the point (x,y) = (7,10)\r\n" );
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document.write( "A. Z = 10x + 10y\r\n" );
document.write( "B. Z = 5x + 2y\r\n" );
document.write( "C. Z = 2x + 8y\r\n" );
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document.write( "Now we'll have to try each of these out to find out if\r\n" );
document.write( "the maximum value of Z occurs at the point (7,10)\r\n" );
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document.write( "corner point |  x  |  y  |      z = 10x + 10y     |\r\n" );
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document.write( "   (0,37/3)  |  0  |37/3 |  10(0)+10(37/3)= 370/3 = 123.33...   \r\n" );
document.write( "    (0,0)    |  0  |  0  |  10(0)+10(0)   =     0\r\n" );
document.write( "   (12,0)    |  12 |  0  |  10(12)+10(0)  =   120\r\n" );
document.write( "    (7,10)   |  7  | 10  |  10(7)+10(10)  =   170 \r\n" );
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document.write( "This is a correct one, since 170 is the largest o\r\n" );
document.write( "value and that occurs at (7,10).  Let's check the other\r\n" );
document.write( "two:\r\n" );
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document.write( "corner point |  x  |  y  |      z = 5x + 2y     |\r\n" );
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document.write( "   (0,37/3)  |  0  |37/3 |  5(0)+2(37/3)= 74/3 = 24.66...   \r\n" );
document.write( "    (0,0)    |  0  |  0  |  5(0)+2(0)   =    0\r\n" );
document.write( "   (12,0)    |  12 |  0  |  5(12)+2(0)  =   60\r\n" );
document.write( "    (7,10)   |  7  | 10  |  5(7)+2(10)  =   55\r\n" );
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document.write( "No, that's not an answer, because 55, which occurs at\r\n" );
document.write( "(7,10), is not the largest value. Let's try the third one:\r\n" );
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document.write( "corner point |  x  |  y  |      z = 2x + 8y     |\r\n" );
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document.write( "   (0,37/3)  |  0  |37/3 |  2(0)+8(37/3)= 296/3 = 98.66...   \r\n" );
document.write( "    (0,0)    |  0  |  0  |  2(0)+8(0)   =    0\r\n" );
document.write( "   (12,0)    |  12 |  0  |  2(12)+8(0)  =   24\r\n" );
document.write( "    (7,10)   |  7  | 10  |  2(7)+9(10)  =  104\r\n" );
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document.write( "This is a correct answer, too since 104 is the largest of the\r\n" );
document.write( "four values and that occurs at (7,10). \r\n" );
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document.write( "So the answer is  A and C\r\n" );
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document.write( "Edwin
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