The demand values for the following 4 weeks for a company is as follows: 300, 200, 400, 430. The weekly regular time production capacity is 260 units. At each week up to 150 more units can be produced in over time with an additional cost of $40 over the regular time production costs. 15% of the produced units become scrap due to quality problems. There is an inventory cost of $12 per unit per quarter. 150 units are available at the beginning of week1 and the company wants to have at least 200 units at the end of week4. Formulate a linear programming model that can be used to minimize the total cost of meeting the next four weeks' demand.

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