document.write( "Question 1130500: For values of x and y defined by the region defined by the inequalities 2x+y>120, y>x and y<2x, find the minimum value of V when V=5x+4y-100. Thank you :D \n" ); document.write( "

Algebra.Com's Answer #747198 by ikleyn(52787) $\"\"$ $\"About$

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document.write( "The region of the interest is shown in the plot below.\r\n" );
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document.write( "It is infinite area in the first quadrant, bounded by the 3 straight lines: red, green and blue.\r\n" );
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document.write( "Plot  2x+y = 120 (red),  y = x (green) and y = 2x (blue)\r\n" );
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document.write( "To find the minimum of the given function V(x,y) = 5x + 4y - 100,  you need to calculate its values in the corner point of the gerion\r\n" );
document.write( "and the choose that corner point where the value of the function is minimal.\r\n" );
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document.write( "The corner points are  P1 = (40,40)   and  P = (30,60).\r\n" );
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document.write( "The values of the function V are:  at P1  V = 5*40 + 4*40 - 100 = 260   and\r\n" );
document.write( "                                   at P2  V = 5*30 + 4*60 - 100 = 290.\r\n" );
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document.write( "The minimum value of V over the region is 260; it is achieved at the point P1.\r\n" );
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\n" ); document.write( "\n" ); document.write( "To see many other similar problems solved by the Linear Programming method, look into the lesson\r
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