An oil company owns two refineries. The daily production limits and operating\r\n" );
document.write( "costs for each refinery are given in the table below. An order is received for\r\n" );
document.write( "1540 barrels of high-grade oil, 1650 barrels of medium-grade oil, and 2860\r\n" );
document.write( "barrels of low-grade oil. How many days should each refinery operate so that\r\n" );
document.write( "the order can be filled at the least cost?\r\n" );
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document.write( " Refinery 1 Refinery 2\r\n" );
document.write( "High-grade oil (barrels) 110 220\r\n" );
document.write( "Medium-grade oil (barrels) 220 110\r\n" );
document.write( "Low-grade oil (barrels) 330 220\r\n" );
document.write( "Operating cost (barrels) 14,000 8,000\r\n" );
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document.write( " x = number of days refinery 1 should operate.\r\n" );
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document.write( " y = number of days refinery 2 should operate.\r\n" );
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document.write( "Constraints:\r\n" );
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\r\n" );
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document.write( "Objective (money intake) Function: P = 14000x + 8000y\r\n" );
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document.write( "Find all the intercepts and points of intersections of all 6 lines --\r\n" );
document.write( "three slanted boundary lines, 1 vertical y-axis boundary line, whose\r\n" );
document.write( "equation is x = 0, and 1 horizontal x-axis boudary line whose equation\r\n" );
document.write( "is y = 0.\r\n" );
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document.write( "{The equation of the line parallel to one of the axes is an equation in \r\n" );
document.write( "terms of the other letter, the letter of the other axis.]\r\n" );
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\r\n" );
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document.write( "which when simplified are\r\n" );
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\r\n" );
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document.write( "You can find all these points by all the methods you've learned in\r\n" );
document.write( "algebra using the substitution or the addition method. I found more \r\n" );
document.write( "of the points than I needed to in order to get the answer to this \r\n" );
document.write( "problem. I only needed to find the lower corner points, since the\r\n" );
document.write( "optimum value is always at one of the corner points. \r\n" );
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document.write( "We'll substitute these corner points of the bottom vertices of an\r\n" );
document.write( "infinitely-large polygon, which are marked with red dots below: \r\n" );
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\r\n" );
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document.write( "The feasible region is the infinite area on or above all 3 slanted lines \r\n" );
document.write( "and the x-axis, and on or to the right of the y-axis.\r\n" );
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document.write( "The objective function is always the money coming in or the money going out. In\r\n" );
document.write( "this case it's going ouit. It's the function C = 14000x + 8000y. We evaluate it\r\n" );
document.write( "at all the 4 red points, the only ones we needed to find the coordinates for.\r\n" );
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document.write( "Corner | C= \r\n" );
document.write( "point | 14000x+8000y=\r\n" );
document.write( "--------|--------------\r\n" );
document.write( "(0,15) | $120000\r\n" );
document.write( " (4,7) | 112000\r\n" );
document.write( " (6,4) | 115000\r\n" );
document.write( "(14,0) | 196000 \r\n" );
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document.write( "So the winner is the point (4,7) with a cost of only $112000.\r\n" );
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document.write( "So the best plan is to operate refinery 1 for 4 hours and operate\r\n" );
document.write( "refinery 2 for 7 hours. \r\n" );
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document.write( "x = 4 days refinery refinery 1 should operate.\r\n" );
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document.write( "y = 7 days refinery 2 should operate.\r\n" );
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document.write( "Least Cost: $112,000\r\n" );
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document.write( "Edwin
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document.write( "![\"\"](\"/images/stars/stars-13.gif\")
