Consider the linear program: Maximize z = x1 + 3x2

subject to: x1 + x2 8

-x1 + x2 4

x1 6

x1 0, x2 0.

ii) the shadow prices on the three constraints

iii) the range on the objective coefficient of each variable, holding the coefficient of the other variable at its current value, for which the solution to part (i) remains optimal;

iv) the range on the availability of each resource, holding the availability of the other resources at their current values, for which the shadow prices in part (ii) remain optimal.