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A stockist has to supply 400 units of a product every Monday to his customers. He gets the product at Rs. 50 per unit from the manufacturer.

The cost of ordering and transportation from the manufacturer is Rs. 75 per order. The cost of carrying inventory is 7.5% per year of the cost of the product. Find: i. The economic lot size ii. The total optimal cost (including the capital cost) iii. The total weekly profit if the item is sold for Rs. 55 per unit

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Demand D = 400 units/week = 400×52 = 20800 units/year

Unit cost Cp = Rs. 50

Inventory holding costs Ch = 7.5% of Cp

Cost of each order Co = Rs. 75

i. Economic Lot Size :

Q^*=√(2.D.CoCh)

=√(2.D.CoCp.I )

=√(2×20800×7550×0.075 )

= 912 units

ii. Total optimal cost (including capital cost) :

Cost = D×Cp + √(2.D.Ch.Co)

= 20800×50 + √(2×20800×50×0.075×75)

= Rs.1043420.526 per year

= Rs.20065.78 per week

iii. Weekly profit:

Profit = selling price × unites sold – cost price per week

= 55×400 – 20065.78

= Rs.1934.22 per week