Q$1)(30$ pts$)$ A company operates a high$-$tech drone for package deliveries. At the beginning of each week, the drone is either operational or non$-$operational. If the drone successfully completes deliveries throughout the week, it generates $\backslash (\backslash$$ $100\backslash )$ in revenue. If it breaks down during the week $($i$.$e$.,$ becomes non$-$operational$),$ it generates no revenue. If the drone is operational at the beginning of a week, the company can choose to perform routine servicing to reduce the chance of a breakdown. If servicing is done, the drone has a $0\mathrm{.}4$ probability of becoming non$-$operational during that week. If servicing is not chosen, the probability of failure rises to $0\mathrm{.}7.$ Routine servicing costs $\backslash (\backslash$$ $20\backslash )$ per week. If the drone is non$-$operational at the beginning of a week, the company must either repair or replace it$.$ Both options are immediate. A repair costs $\backslash (\backslash$$ $40\backslash ),$ and the repaired drone has a $0\mathrm{.}4$ probability of failing during the week. Replacing the drone costs $\backslash (\backslash$$ $90\backslash ),$ but a new drone is guaranteed to function properly for the next week. Using dynamic programming, determine the optimal servicing, repair, and replacement policy to maximize the expected net profit over a four$-$week period, starting with the drone operational at the beginning of the first week. Write down states, stages, decisions and recursion function clearly.