$-$ Each week she must decide how many flowers to make. A knitted flower can be sold for $\backslash (\backslash$$ $12\mathrm{.}50\backslash ).$

$-$ She prefers not to store more than $8$ flowers at her home at any point in time.

$-$ Each week there is $\backslash (10\backslash \%\backslash )$ chance one customer wants to buy a flower, a $\backslash (25\backslash \%\backslash )$ chance she sees a demand of $2$ flowers, a $\backslash (35\backslash \%\backslash )$ chance she sees a demand of $3$ flowers, a $\backslash (10\backslash \%\backslash )$ chance she sees a demand of $4$ flowers, and a $\backslash (20\backslash \%\backslash )$ chance no customers are interested in buying her flowers.

$-$ She never sees a demand of more than $4$ flowers in any given week. If she has no flowers when a customer comes, the customer leaves without buying flowers.

$-$ On those woeks that she chooses to make flowers, she must pay a total fixed cost of $\backslash (\backslash$$ $15\backslash )$ for renting the space to make the flowers. In addition, it costs her $\backslash (\backslash$$ $8\backslash )$ to make one flower.

$-$ Flowers not sold at the end of the day can be donated to charity for $\backslash$$$3$ tax credit.

$-$ Formulate this problem as a Markov decision process, in which the objective is to maximize the total expected income over the next $3$ weeks $($assume there are only $3$ woeks left before the farmer's market closes for the winter$).$ Clearly indicate the $5$ basic components of this MDP$.$

$-$ Update: Both of the following interpretations are acceptable:

$($a$)$ Flowers not sold at the end of the three weeks can be donated to charity for $\backslash (\backslash$$ $3\backslash )$ tax credit.

$($b$)$ Flowers not sold at the end of every week can be donated to charity for $\backslash (\backslash$$ $3\backslash )$ tax credit.

Please write out complete answers with labels