A manufacturer buys cardboard boxes from a supplier. The annual demand is $40,000$ boxes and is uniformly distributed. The boxes cost $$5$ each. The estimated order cost is $$10,$ and the carrying cost rate is $20\%$ per year.A manufacturer buys cardboard boxes from a supplier. The annual demand is $40,000$ boxes and is uniformly distributed. The boxes cost $$5$ each. The estimated order cost is $$10,$ and the carrying cost rate is $20\%$ per year.