$3.$ Sherwin$-$Williams would like to develop a master production schedule for its popular $$Harmony Interior Acrylic Latex$$ paint over the next $4$ quarters. The quarterly forecast $($in $1000$ gallons$)$ for the $$Harmony Interior Acrylic Latex$$ paint is provided in the table below. Sherwin$-$ Williams currently has $30$K gallons of $$Harmony Interior Acrylic Latex$$ paint on hand. Whenever a production is scheduled in a quarter, the lot size for that production is always $80$K per quarter. As the production manager of Sherwin$-$Williams, using time$-$phased record, develop a master production schedule to minimize the ending inventory $($i$.$e$.,$ the inventory at the end of the $4$th quarter$).(10$ points$)$