We performed a simulation study of a simple heat engine as it undergoes Carnot-type cyclic motion in a finite time over a wide range of piston speeds. There exists a specific piston speed at which the power delivered by the engine is maximum (Pmax) and its corresponding efficiency is slightly larger than half of the Carnot efficiency (1/2 etac). An optimization criterion leads to a trade-off between high power and high efficiency with respective values of 4/5 Pmax and 3/4 etac. In addition, we found the time taken at the optimized state to be twice the time taken when operating at maximum power.