1. (a) Suppose that you formulate a Linear Programme (LP) with: three deci 0 sio
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1. (a) Suppose that you formulate a Linear Programme (LP) with: three deci 0 sion variables b, s and g; objective to maximise 30b +50s+80g; and ten constraints. On solving the LP, the solver returns the information shown in Table 1 for constraints (3) and (5) Constraint 3) 6b + 3s300000 (5) b2 2800 Slack or Surplus Dual Price 0.0000 16.66667 00.0000 0.00000 Table 1: Constraints and solver output Which, if either, of these constraints is binding (i.e., tight) and why? Explain what is meant by the 16.66667 dual price for constraint (3).Explanation / Answer
Binding Constraints are those which becomes equality for the optimal solution of the variables, in other words, any change in its value will bring change in the optimal solution. If we analyze it deeply, it suggests the slack or surplus variable for binding constraint will be zero, because if we put the optimal value of the decision varibales in binding constraints it becomes equality.
From the final table, it can be seen that Constraint 3 is a binding constraint.
b) Dual Price of any constraints gives us the idea about the impact of the change in right-hand side value of the constraint in the objective function. To be very precise dual price represents the amount the objective would improve if the RHS value of the constraint is increased by one unit.
So, from the table, it suggests that if we increase the RHS value of the 3rd constraint by 1 unit then the objective will improve by 16.66667 units.
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