Duality of Profit Maximization and Expenditure Minimization

Part 1

Arjun runs a recycling plant that turns plastic waste into pellets. The recycling plant's weekly output, in tonnes of pellets, is Q = pfunc, where L is the number of hours of sorter labor and K the number of hours of shredder time used per week. Arjun sells each tonne of pellets for $price, pays $wage per hour of sorter labor and $rent per hour of shredder time, and currently uses lnow hours of sorter labor and know hours of shredder time a week. Both inputs can be changed freely, and all markets are competitive. At the profit-maximizing choice of L and K, what is the total weekly cost of labor and capital, to the nearest dollar?

Part 2

Arjun runs a recycling plant that turns plastic waste into pellets. The recycling plant's weekly output, in tonnes of pellets, is Q = pfunc, where L is the number of hours of sorter labor and K the number of hours of shredder time used per week. Arjun pays $wage per hour of sorter labor and $rent per hour of shredder time, and currently uses lnow hours of sorter labor and know hours of shredder time a week. Both inputs can be changed freely, and all markets are competitive. Arjun needs to produce exactly output tonnes of pellets per week at the lowest possible cost. What is the lowest weekly cost of producing that output, to the nearest dollar?