Perform the sensitivity analysis for the Mining Problem 3.2 (Pag. 52). Formulati
ID: 3121427 • Letter: P
Question
Perform the sensitivity analysis for the Mining Problem 3.2 (Pag. 52). Formulation is below, graphical solution is in the book Provide calculations to find: - Shadow Prices for all 6 constraints - Allowable inc./dec. for NOT-BINDING constraints only - Unit prices and allowable inc./dec. for c_1 and c_2. Minimize Z = 3x_1 + 9x_2 Subject to: 40x_1 + 15x_2 greaterthanorequalto 10 [1] 14x_1 + 35x_2 greaterthanorequalto 140 [2] x_1 lessthanorequalto 5 [3] x_2 lessthanorequalto 5 [4] x_1, x_3 greaterthanorequalto 0. [5], [6]Explanation / Answer
From Graphical solution we come to know about the optimum value of z and it is Zmin=3(5)+9(2)=33
For first constraint when rhs is 99 or 101 then x2 will be equal to 1 or 3 respectively.
Therefore optimum value will be 24 or 42. Hence shadow price for this constraint is 9.