The production manager for the classic boat corporation must determine how many units of the classic $21$ model to produce over the next four quarters. The company has beginning inventory of $100$ classic $21$ boats, and demand for the four quarters is $2000$ units in quarter $1,4000$ units in quarter $2,3000$ units in quarter $3,$ and $1500$ units in quarter $4.$ The firm has limited production capacity in each quarter. That is$,$ up to $4000$ units can be produced in quarter $1,3000$ units in quarter $2,2000$ units in quarter $3,$ and $4000$ units in quarter $4.$ Each boat held in inventory in quarters $1$ and $2$ incurs an inventory holding cost of $$250$ per unit; the holding cost for quarters $3$ and $4$ is $$300$ per unit. The production costs for the first quarter are $$10,000$ per unit; these costs are expected to increase by $10\%$ each quarter because of increases in labor and material costs. Management specified that the ending inventory for quarter $4$ must be at least $500$ boats. a$.$ formulate a linear progrsamming smodel that can be used to determine the production schedule that will minimize the total cost of meeting demand in each qurter subject to production capacities in each quarter and also in required ending inventory in quarter $4.$ b$.$ solve the linear programming formulated in part a then develope a table that will show for each quarter the number of units to manufacture the ending inventory and the cost incurred. c$.$ imterpret each of the dual values corresponding to the constraintsdeveloped to meet demand in each quarter. based on these dual values, what advise would you give the production manager? d$.$ interpret each of the dual valuescorresponding to production capacity in each quarter. based on each of these dual values what advise would you give the production manager