Past exam of the Probability, statistics and options II course of the University of Oxford / 2007 / T / 2 / c / ii

Let the third profit coefficient be $c_3$. For the same basis, the resource dual prices solve $2y_1+y_2=3$ and $5y_1+3y_2=c_3$, givingDual feasibility requires $y_1,y_2\ge 0$ and $3y_1+2y_2\ge 4$. These inequalities are $c_3\le 9$, $c_3\ge 15/2$ and $c_3\ge 7$, respectively. HenceThe production vector is unchanged because the resource constraints are unchanged. Equality at a boundary can allow additional optimal solutions.