A stockist wishes to optimize the number of perishable items he needs to stock in any month in his store. The demand distribution for this perishable item is: The stockist pays Rs.$$70$$ for each item and he sells each at Rs.$$90.$$ if the stock is left unsold in any month, he can sell the item at Rs.$$50$$ each. There is no penalty for unfulfilled demand. To maximize the expected profit, the optimal stock level is:

A firm is required to procure three items $$(P, Q$$ and $$R).$$ The prices quoted for these items (in Rs.) by suppliers $${S_1},{S_2},$$ and $${S_3}$$ are given in table. The management policy requires that each item has to be supplied by only one supplier and one supplier supply only one item. The minimum total cost (in Rs.) of procurement to the firm is:

A $$60mm$$ long and $$6mm$$ thick fillet weld carries a steady load of $$15kN$$ along the weld. The shear strength of the weld material is equal to $$200MPa.$$ The factor of safety is

A cylindrical shafts is subjected to an alternating stress of $$100MPa.$$ Fatigue strength to sustain $$1000$$ cycles is $$490MPa.$$ If the corrected endurance strength is $$70MPa,$$ estimated shaft life will be