The Blast company prices GC game consoles at $650 per unit. GameCore sells the GCs at $875. Annual demand at this retail price turns out to be 400,000 units. GameCore incurs ordering, receiving, and transportation costs of $12,000 for each lot of GCs ordered. The annual holding cost used by the retailer is 25 percent.

a)What is the optimal lot size that GameCore should order?

b)The Blast company has discounted GCs by $50 for the short term (about the next two weeks). Game Core has decided not to change the retail price but may change the lot size ordered from Blast. How should GameCore adjust its lot size given this discount? How much does the lot size increase because of the discount?

Please show formula used and detailed explanation.