operations research question. please do by hand and show work. thank you.

1. Anderson Manufacturing Company (AMC) has contracted to deliver hotel windows over the next 6 months. The demands for each month are 100, 250, 190, 140,220, and 110 units, respectively. Production cost per window varies from month to month depending on the cost of labor, material, and utilities. Acme estimates the production cost per window over the next 6 months to be $50, $45, $55, $48, $52, and $50, respectively. To take advantage of the fluctuations in manufacturing cost, AMC may elect to produce more or less than is needed in a given month. This, however, will incur inventory costs at the rate of $8 per window per month or a shortage cost of $12 per window per month. All demand must be met by the end of month 6. Formulate an LP that minimizes AMS's total cost during the next six months