Morgan Inc. is planning the purchase of one of the component parts it needs for its finished product. The anticipated demands for the component for the next $12$ periods are shown in the following table. The cost to order the component $($labor$,$ shipping, and paperwork$)$ is $$150.$ The cost to hold these components in inventory is $$1$ per component per period. The price of the component is expected to remain stable at $$12$ per unit for the next $12$ periods, and no quantity discounts are available. The maximum order size is $1,000$ units.

Time Period $123456789101112$

Demand $2020304014036050054046080020$

$($a$)$ Formulate a model to minimize the total cost $($in $$)$ of satisfying Morgan Inc.$\text{'}$s demand for this component.

Let xt $=$ amount to order at the start of period t$,$ Ht $=$ amount to hold in inventory at the end of period t$,$ and

Yt $=1$ if an order is placed at the start of period t $0$ otherwise

for t $=1,2,3,...,12.$

Min $(\_\_\_\_)($x$1+$ x$2+...+$ x$12)+(\_\_\_\_)($H$1+$ H$2+...+$ H$12)+(\_\_\_\_\_\_)($Y$1+$ Y$2+...+$ Y$12)$

Period $1$ Demand

Please show using excel