This paper studies a multi-hop decode-and-forward (DF) simultaneous wireless information and power transfer (SWIPT) system where a source sends data to a destination with the aid of multi-hop relays which do not depend on an external energy source. To this end, we apply power splitting (PS) based SWIPT relaying protocol so that the relays can harvest energy from the received signals from the previous hop to reliably forward the information of the source to the destination. We aim to solve two optimization problems relevant to our system model. First, we minimize the transmit power at the source under the individual quality-of-service (QoS) threshold constraints of the relays and the destination nodes by optimizing PS ratios at the relays. The second is to maximize the minimum system achievable rate by optimizing the PS ratio at each relay. Based on convex optimization techniques, the globally optimal PS ratio solution is obtained in closed-form for both problems. By setting the QoS threshold constraint the same for each node for the source transmit power problem, we discovered that either the minimum source transmit power or the maximum system throughput can be found using the same approach. Numerical results demonstrate the superiority of the proposed optimal SWIPT PS design over conventional fixed PS ratio schemes.