Tan Manufacturing Inc, will produce double-glazed windows to fulfill deliveries over the next six months. Monthly demands for the six-month period are 100,250,190,140, and 220 , respectively. The production cost per double-glazed window varies month by month due to labor and material usage costs. Tan Inc. estimates the production costs for the next six months to be 50,45,55,48,52, and 50p per double-glazed window, respectively. To take advantage of fluctuations in production costs, Tan Inc. can produce to meet not only the current month's demand but also to stock for future periods. In such a case, a storage cost of 8p per double-glazed window per month will be added to the end-of-month inventory values.

a) Formulate a linear programming model to determine Tan Inco's optimal production schedule.
b) Solve the problem assuming an initial inventory of 25 double-glazed windows at the beginning of the first month.