Consider Example 3.5 (with recourse function given in XXXXXXXXXXwith a single first-stage decision x with first-stage cost c · x and with ξ = 1 or 2 with probability of 1/2 each. Show: a) If x must be...

Consider Example 3.5 (with recourse function given in (3.3.1)) with a single first-stage decision x with first-stage cost c · x and

with ξ = 1 or 2 with probability of 1/2 each. Show:

a) If x must be integer, then EV > WS for any value of c ≥ 0 .

(b) If x is continuous, then EV = WS for 0 ≤ c ≤ 1 and EV > WS for c > 1 . Beware that y is always integer; the discussion here concerns the effect of x ’s being integer or not.