A company is preparing a production plan for an item to minimize total cost for the next three months. The holding cost applied to the inventory at the end of each month is $3/item. The demand for the next three months is expected to be 500,400, and 700 units. The item can be produced using resources at plant A, at plant B and at a third party facility. The capacity and costs are shown below. Capacity Costs Plant A 250 Items/month $25/item Plant B 300 Items/month $27/item Third Party 100 Items/month $31/item Formulate the LP problem What is the optimal solution? provide the value of each decision variable and the objective function. Find the highest positive dual value and clearly explain what it means.