Q$2)$ For a four$-$month inventory problem, the demand and cost data for each month are provided in the following table. The products are produced in $5$ batches. The initial inventory available at the beginning of the first month is $5$ units and it is desired to have $5$ units at the end of the $4^{th}$ month.

$\backslash$table$[[\backslash$table$[[$Period$],[($Month$)]],\backslash$table$[[$Demand$],[($in units$)]],\backslash$table$[[$Setup Cost$],[($in $$/$batch$)]],\backslash$table$[[$Production Cost$],[($in $$/$unit$)]],\backslash$table$[[$Holding Cost$],[($in $$/$unit$/$month$)]]],[1,10,60,2\mathrm{.}5,0\mathrm{.}6],[2,5,70,3,0\mathrm{.}8],[3,15,50,2\mathrm{.}6,0\mathrm{.}7],[4,15,80,3\mathrm{.}0,0\mathrm{.}9]]$

a$.$ Use dynamic programming to find the optimal policy and minimum total cost $($use backward recursion$).($pdf file$)$

b$.$ Find the optimal policy by using dynamic programming in EXCEL $($Hint: It is very similar to the shortest path DP Excel solution. But you need to find a way to add costs$).$

Q$3)$ Consider that in the previous question, the company's production and storage capacity is at most $6$ and $4$ batches, respectively.

a$.$ Use dynamic programming to find the optimal policy and minimum total cost $($use forward recursion$).($pdf file$)$

b$.$ Find the optimal policy by using dynamic programming in EXCEL.

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