The Optimal Solution of the Linear Programming Problem Is at the Intersection

Essay

The optimal solution of the linear programming problem is at the intersection of constraints 1 and 2.
$$\begin{array} { l l } \operatorname { Max } & 2 x _ { 1 } + x _ { 2 } \\\text { s.t. } & 4 x _ { 1 } + 1 x _ { 2 } \leq 400 \\& 4 x _ { 1 } + 3 x _ { 2 } \leq 600 \\& 1 x _ { 1 } + 2 x _ { 2 } \leq 300 \\& x _ { 1 } , x _ { 2 } \geq 0\end{array}$$
a.Over what range can the coefficient of x₁ vary before the current solution is no longer optimal?
b.Over what range can the coefficient of x₂ vary before the current solution is no longer optimal?
c.Compute the dual prices for the three constraints.