Han Solo projects the firm's aggragate requirements over the next three months to be : 100,200, and 200 units of their flagship products. His operations manager can allocate regular and overtime capacities for poroduction, but not at the level of demeand. Regualr production costs $5000 per unit with 150 units per month. Overtime cost $8000 per unit, with only a maximum of 30 capacity per month. Invenotry carrying costs is $1,200 per month per unit. But backordering costs have penalties of $2000 per unit per month. Determine the production and inventory plan that would meet the demand for the next three months at minimum cost. Determine cost of your plan. Assume zero inventory at the beggining.