Bata India Ltd$.$ has a Master Schedule for running shoe production in its facility in lot sizes of $40$ Pairs of units. The initial inventory has $45$ units and the demand forecast is $20,20,30,20,20,13,15$ and $20$ units respectively for eight weeks. The company has received orders for $22$units in week $1,9$ units in week $2,4$ units in week $3,15$ units in week $4$ and $5$ units in week $5.$ Setup an MPS and find the ATP inventory values for week $1$ through $8.$