MintFactory is one of the clothing factories supplying dresses to MintHouse. The workers at MintFactory work 25 days a month, with a regular working hour of 8 hours per day. Any time beyond that is considered overtime, which is limited to 20 hours per month per worker. Regular-time pay is $5 per hour and overtime is $8 per hour. MintFactory currently employs 250 workers. Each dress requires 20 hours of labour input. It costs $2 to carry a dress in inventory for a month. Materials cost per dress is $8 and the dresses are sold to its customers at a price of $20 each. MintFactorys subcontractor charges $500 for a bulk order of 50 dresses and is able to supply a maximum of 150 dresses per month. The subcontractor takes in only bulk order quantities from MintFactory. MintFactory begins with 200 dresses in stock at the start of January. The supply chain manager at MintFactory is tasked to ensure that there are at least 600 dresses in stock in end December.

Solve the following aggregate planning problem: Assuming no backlogs and no hiring/firing of workers during the planning period, formulate the aggregate planning problem for MintFactory for time period t, using Linear Programming technique. Demand is given to be Dt. You should state the necessary decision variables, objective function and constraints in your answer.