Balaji Soaps is a manufacturing company of different types of soaps. The product portfolio of the

company includes $100$ percent Natural & Aromatherapy Soaps, Toilet Soaps, Fancy Soaps, Sandal Soaps,

Handmade Soaps, Specialty Soaps, and Herbal Soaps.

The annual usage of raw material is $51500$ units for the company and the raw material cost per unit is

Rs$\mathrm{.}52.$ The ordering cost is Rs$.220$ per order and the carrying cost is $22$ percent of the average value of

the raw material. The supplier of raw material has recently introduced a discount of $5$ percent on the price

of raw material for orders of $1650$ units and above. Calculate the company$$s EOQ prior to the

introduction of discounts. Should the company opt for availing the discount? What would be the optimal

order size if the company opts to avail the discounts?