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Problem 1 (25 points) We model the cash flow in a company with a central office and a single sales outlet. The central office holds C(t) dollars of cash at time t (measured in weeks) and provides 80% of its current cash per week to the sales outlet. The sales outlet holds S(t) dollars in cash at time t, has an income of 30% of its current cash per week, and returns 90% of its cash per week to the central office. The central office and the sales office have fixed costs of $100,000 and $60,000 per week, respectively. 1. Draw a graphical compartment model for the cash at the central office and the sales outlet with inflows and outflows that represent the situation outlined above. 2. Derive a differential-equations model for (C,S)(t) based on the compartment model