A company sells bricks, produced in a normal monthly 8-hour shift or an extended monthly 12-hour shift. An 8-hour shift can produce 6000 units per month at a cost of $110000 per month. The 12-hour shift costs $180000 per month and can produce 8,000 units monthly. The company can also decide not to produce any bricks in a month. This means that they can only use one of the three options per month. For example , if they use 8-hour shifts in a certain month they need to use 8-hour shifts the entire month. The same with 12-hour shifts and months with no production.

The raw materials to produce a unit is $0.50. If the production exceeds 7000 units, contractors need to be hired to complete the production at a price of $30000. If the company decides to produce bricks in a certain month it should at least be 2000 units.

Changing from an 8-hour shift to a 12-hour shift the next month will have a setup cost of $15000. Changing from a month with no production to a month with production will cost an additional $ 10,000. Changing from a 12-hour shift to an 8-hour shift will have no additional cost. Changing from a month with production to a month with no production will have no additional cost.

The production process is currently running on a normal 8-hour shift. Holding inventory will cost $2 per month per unit. Assume that the cost of inventory for any month is related to the amount in stock at the end of that month. There are currently 500 units in stock and the inventory cost for the current stock does not need to be taken into consideration at the start of month 1. The amount in stock at the end of month 12 should be at least 3000 units.

The demand for each month is as follows: Month 1: 8000 Month 2: 6500 Month 3: 6500 Month 4: 2100 Month 5: 500 Month 6: 6500 Month 7: 2000 Month 8: 6800 Month 9: 8300 Month 10: 8000 Month 11: 8000 Month 12: 2000.

Optimize a linear programming production plan for the 12-month period using Excel Solver.