For eachbinRm, letξ(b) denote the optimal objective function value for

the following linear program:

maximizec' x

subject toAx ≤ b0

x ≥.

Suppose thatξ(b)< ∞for allb. Show that the functionξ(b) is concave (a

functionfon Rmis calledconcaveiff(tx+(1−t)y)≥ tf(x)+(1−t)f(y)

for allxandyin Rmand all 0< t <1).Hint: Consider the dual problem.

Isn't there only one objective value? Not one for each b value?