Following table shows the forecasts and customer orders for two products.

$\backslash$table$[[,$Week$],[,1,2,3,4,5,6,7,8,],[\backslash$table$[[$Product$],[1]],$Forecast,$3,3,3,3,3,4,4,4,],[$Customer orders,$8,1,4,5,4,1,4,-,],[\backslash$table$[[$Product$],[2]],$Forecast,$1,000,1,000,1,000,1,000,2,000,2,000,2,000,2,000,],[$Customer orders,$1,200,800,300,200,100,-,-,-,]]$

Products $1$ and $2$ are manufactured in batches $($or multiples of batches if needed$)$ of $12$ and $2,500$ units, respectively. At the beginning of the first week, $10$ units of product $1$ and $1,600$ units of product $2$ are available.

$($a$)$ For each product, determine the MPS and POH values of the weeks.

$($b$)$ For product $1,$ determine the ATP$-$discrete values of the weeks. Can the sales department promise to a new customer order of four units in week $5?$ If not, what can be done?

$($c$)$ For product $2,$ determine the ATP without look$-$ahead and the ATP with look$-$ahead values of the weeks.