2. Use the simplex method to solve the following linear programme. maximise 7x + 8x2 - 2x3. subject to 7x1 + 4x2 + 2x3 68, 6x14x22x3 36, X1 0, x > 0, X3 0. 3. The following table gives the choices of two individuals, Chloe and Micah, from the menu M = {A, B, C, D}, and each submenu of M with at least two elements. menu or Chloe's submenu choice ABCD ABC ABD ACD BCD AB AC AD BC BD CD BC D D CD B AC A BD C Micah's choice BD C ABD CD BD A A AD B BD D (a) For each of Chloe and Micah, determine whether their choice from M satisfies (1) the contraction condition; (II) the expansion condition. (b) Is either Chloe's choice from M or Micah's choice from M reasonable? Briefly jus- tify your answer.