John spends off days from Skyrim running his custom jewelry shop. He categorizes jewelry into two categories: protective small talismans $(t)$ and big cursed charms $(c)$. Talismans typically sell for 12 gold while charms go for 15. Costing is unique in Targon as detailed below: One talisman costs 2 Gold to make No matter how many talismans are there, John needs to pay 1 Gold in offering to the protectors of Skyrim. The total cost of talismans is then squared to account for area and labor costs. One charm costs 3 Gold to make John gets 2 Gold flat, regardless of number of charms produced, as a discount for putting to use trapped Black Mist fiends. The total cost of charms is then squared to account for area and labor costs.Good relations with shady business dealer Tahm Kench cuts John's total cost in the amount equivalent to 1 talisman and twice the number of charms, squared.

a) What are the cost, revenue, and profit functions for John's business? 

b) How much of each should he sell (both rounded up) to gain maximum profit? [Use the second derivative test.