PLEASE DON'T CODE.

I have a garden that has a length of $10$ meters. I would like to grow three types of plants:

Plant $1$: tomatoes

Plant $2$: fava beans

Plant $3$: corn

The garden is organized in rows and each row of tomatoes occupies a width L$1=2$ meters, each row of fava beans a width L$2=3$ meters and each row of corn a width L$3=2$ meters. I give each row of tomatoes a value v$1=10,$ each row of fava beans a value v$2=3$ and finally each row of corn a value v$3=7.$ Regardless of the value I give to each plant, I have to plant at least one row of fava beans and not more than two rows of tomatoes $($it$$s my wife who asks me and I have no choice but to obey$).$ I would like to determine the number of rows to assign to each plant in order to maximize the total value of my garden, noting that it is possible to assign no row to tomatoes and corn. To do this, I decide to use dynamic programming.

$($a$)($Define the stages, states, decision variables, and recurrence formula for this problem.

$($b$)$ Solve the problem using dynamic programming. Identify explicitly the optimal decision policy$($s$).$