State whether the following statements are True or False. Give reasons in support of your answers.

(a) The solution of a transportation problem with 5 rows (supplies) and 4 columns (destinations) is feasible if number of possible allocations are 8.

(b) The moving averages of suitable period in a time-series are free from the influences of seasonal and cyclic variations.

(c) If the basic solutions for a system of equations are (-2, 0, 1), (0, 1, 3), (-2, 3, 0), then only (0, 1, 3) is feasible.

(d) In the stepwise selection method of multiple regression model, once a variable enters in the model then it always remains in the model.

(e) An enterprise requires 1000 units per month. The ordering cost is estimated to be 50 per order. The purchase price is 20 per unit and the carrying cost per unit is 10% of it. Then the economic lot size to be ordered is 775.

(a) False
The number of possible allocations in a transportation problem is determined by the product of the number of rows (supplies) and the number of columns (destinations). For a feasible solution, the number of allocations is not necessarily 8. The correct number of allocations is the total number of supply-demand pairs, which is 5 * 4 = 20. Feasibility depends on balancing supplies and demands, not the number of allocations.

(b) True
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