1) Consider the set X = {x E R' / 93x1+34x2 + 26x3 + 18.x4 < 131, x1, x2, 3, X4 E {C (a) Show that xı + x2 + x3 < 2 is a valid inequality for X.

A length of wire that is 160 cm long is cut into two pieces: one to form an equilateral triangle and the other to form a circle. Where do you cut the wire to makes shapes that enclose a maximum amount of area for the two shapes? Where do you cut the wire to enclose a minimum amount of area for the two shapes?