Problem $1.$ ABC Manufacturing produces a perishable product that can be stored for only two

days after the day of its production. $($For example, if a batch of the product is manufactured

on Monday, that batch can be used to meet the demand on Monday, Tuesday, and

Wednesday only, and the remainder of the batch needs to be discarded on Thursday.$)$ The

setup cost ABC incurs per production order is $$100,$ and the holding cost is $$5$ per unit per

day. The demand for the product over the next seven days is shown below.

ABC would like to determine the production plan for this product over the next seven days

$($i$.$e$.,$ how much to produce and when$),$ with the goal of minimizing total setup and inven$-$

tory holding costs. Determine the optimal production plan for ABC. If there are multiple

production plans that yield the optimal cost, show all of them for full credit.