Trendyfashion corporation, a jeweler manufacturer, is known for its flagship product XYZ. They wish to develop a production plan for the product over the next three months. The demand and the production cost for the product for the next three months, labelled as month 1,2 and 3, are provided below in the table 1. Table 2: Demand and production cost of the product over three months Months Demand (in units) Production cost (/per unit) 1 20 13 2 10 14 3 15 15 At the start of each month, the company must decide the production quantity for that month. The quantity produced in a month cannot be used to meet the complete demand of the current month. Thus, we assume the demand of a month can be met by half of production quantity of the given month. At the end of each month, the company incurs a holding cost of 2 per unit on the ending inventory. Moreover, the company has 5 units of the product at the start of first month. Formulate the companys production plan as a linear programming problem.