To explore one impact of the information available by adding sensors in a classical production planning setting, we consider a continuous time infinite horizon lot-sizing model where a single product is manufactured on a single machine. Each time manufacturing restarts, a random production rate is realized, and production continues at this rate until the machine is shut down. Although the rate is random and chosen from an arbitrary set of random rates, it is known as soon as production starts due to the availability of sensor information, so this information could be used to determine when to stop production. However, we show that given the objective of minimizing either average cost per unit time or total discounted cost, it is optimal to produce up to the same inventory level regardless of the realized production rate. We also develop heuristics for the multi-product version of this model.