1. Solve the production problem presented below: [50] The production process of a plant uses a certain raw material. Exogenous influences determine the usage rate of this material. To ensure continuous production, the company keeps an inventory of the raw material. A supply delay of 5 months occurs between the ordering of additional raw material and its arrival in the inventory. In an attempt to guard against inventory shortages, the management has decided to employ the formal policy of ordering exactly the amount of material consumed, i.e. order rate = usage rate. Assume the exogenously determined usage rate increases linearly with time. Your solution must show the two types of flows and the concomitant equations. Total=50