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min max of w = 2x − 3y + 4z when 3x + 5y + 7z = 10 and x + 2y + 5z = 6

Source: 2005 Bosnia & Herzegovina JBMO TST p1

May 27, 2020
minmaxalgebrainequalities

Problem Statement

Non-negative real numbers x,y,zx, y, z satisfy the following relations:
3x+5y+7z=103x + 5y + 7z = 10 and x+2y+5z=6x + 2y + 5z = 6.
Find the minimum and maximum of w=2xāˆ’3y+4zw = 2x - 3y + 4z.
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