This paper discusses an inventory model for a single perishable product with two types of customers, high priority and low priority ones (the former buys only the newest commodity, while the latter buys either one, whether the newest or not), different selling prices reflecting the remaining lifetime of commodity and the constraint of the warehouse capacity (i.e., the capacity of own warehouse, and so the excess inventory are stored in the rental warehouse). Further demands in successive periods are assumed to be independent nonnegative random variables with known distribution functions and high priority and low priority demands are independent. Stock is depleted by high priority demand first and then low priority demand using FIFO issuing policy. Assuming two types of shortage costs, different selling prices, outdating cost purchasing cost, two types of holding costs, an optimal ordering policy to maximize the expected profit is derived.