Cornerstone Ltd carries an item of inventory to which the following data apply:

fixed cost of ordering per batch ................................ £5
expected steady quarterly volume of sales ............. 3,125 units
cost of holding one unit in stock for one year ........ £0.50

Required:

(i) Calculate the minimum annual cost of ordering and stocking the item.
(ii) Calculate to the nearest whole number of units the optimal batch size if the expected steady quarterly volume of sales: first falls to 781 units and second rises to 6,250 units and to state the relationship between the rates of change of sales and the optimal batch size.
(iii) Explain the basis of the derivation of the formula for the optimal batch size which is given in the table of formulae.