Linear Programming

We see that the primal and the dual of linear programming are related mathematically, we can now show that they are also related in economic sense. Consider the economic interpretation of the duality of linear programming – first for a maximization problem and then for a minimization problem. The maximization problem: Consider the following linear programming problem. The optimal solution to this problem dives production of 18 units of Xi and 8 units of x2 per week. It yields the maximum prof of a Rs. 1000, Maximize Z = 40×1 + 35×2, Subject to 2×1 + 3X2 < or = 60, Raw materials constraint per week. 4×1 + 3X2 < or = 96, Capacity constraint per week. x1,x2 > or = 0 The optimal solution to this problem gives production of 18 units of x1 and 8 units of x2 per week. It yields the maximum profit of a Rs. Continue reading

Transportation problem is a particular class of linear programming, which is associated with day-to-day activities in our real life and mainly deals with logistics. It helps in solving problems on distribution and transportation of resources from one place to another. The goods are transported from a set of sources (e.g., factory) to a set of destinations (e.g., warehouse) to meet the specific requirements. In other words, transportation problems deal with the transportation of a single product manufactured at different plants (supply origins) to a number of different warehouses (demand destinations). The objective is to satisfy the demand at destinations from the supply constraints at the minimum transportation cost possible. To achieve this objective, we must know the quantity of available supplies and the quantities demanded. In addition, we must also know the location, to find the cost of transporting one unit of commodity from the place of origin to the Continue reading