A company that makes industrial pumps wants to prepare a master production schedule for June and July. Marketing has forecasted demand of $120$ pump for June and $160$ pumps for July for its major product. These will be evenly distributed over the four weeks in each month: $30$ per week in June and $40$ per week in July as illustrated in the following table. Suppose that there are currently $64$ units of the pump on hand, and that there are some customer orders that have been committed $($booked$)$ and must be filled. Suppose that the economic production quantity is $80$ unites. Every time projected on$-$hand inventory becomes negative, another production lot of $80$ units is added to the table. Calculate the project on$-$hand inventories, planned production, and available to promise inventory $($Explain in detail$).$

$\backslash$table$[[,$Weeks$],[,1,2,3,4,5,6,7,8,],[$Forecast$,30,30,30,30,40,40,40,40,],[\backslash$table$[[$Customer$],[$orders$]],32,21,13,5,3,,,,]]$