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 with 5 rows (supplies) and 4 columns (destinations) is calculated as (m + n - 1) choose (m), where m is the number of rows and n is the number of columns. In this case, it would be (5 + 4 - 1) choose 5, which is 8 choose 5. This is not equal _________ _______ ____ _____ __________ _________ _______ __________ ________.
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