Consider a supply chain with suppliers (S), producers (P), and retailers (R). The supplier takes in raw material at input rate u(t). Raw material that does not meet standards is discarded at rate k and raw material meeting standards is shipped to the producer at rate k. The producer manufactures various products, which are sent to retailers at rate k3. The retailers sell products at output rate y(t) and return products to the producer at rate k4. (a) Draw a three-compartment model to represent this supply chain. (b) Write the differential equations for this model in terms of states xs, ap, and xr.