You are a professor who has a summer business that makes custom sheds. During the three months of operation, you do not know the demand, but you know it will be 1 or 2 sheds for each month, and each choice is equally likely. There is a storage cost of $100 per shed in each month that you have any held over, and the most you can hold over is 3 sheds. Every month that you make any sheds costs you $300 to rent shop space, and each shed costs you an additional $200 in materials. You sell sheds during the summer for $1500 each, and any that are left over at the end of the summer you sell to a woodworker for $200 each. (a) Use probabilistic dynamic programming to determine an optimal production schedule.

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You are a professor who has a summer business that makes custom sheds. During the three months
of operation, you do not know the demand, but you know it will be 1 or 2 sheds for each month, and
each choice is equally likely. There is a storage cost of $100 per shed in each month that you have
any held over, and the most you can hold over is 3 sheds. Every month that you make any sheds
costs you $300 to rent shop space, and each shed costs you an additional $200 in materials. You sell
sheds during the summer for $1500 each, and any that are left over at the end of the summer you
sell to a woodworker for $200 each.
(a) Use probabilistic dynamic programming to determine an optimal production schedule.

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