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

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