Please form a linear program for this problem:

A manufacturer is deciding its production over the next four month planning horizon: - Marketing has forecasted the exact demand for each month (see table below) - Each month's demand must be satisfied (no backlogging, lost sales, etc.) - Production is limited to up to 200 units per month - Up to 100 units can be stored at a holding cost of \$2 per unit per month. Now suppose that there is an additional cost to switching production level from month to month. This cost is $0.50 per unit - for example, if we produce 100 units in month 1 and 200 units in month 2 and 180 units in month 3, we will pay a switching cost of $50 at the end of month 1 and $10 at the end of month 2. (Assume that we can select any initial production level for month 1 without a switching cost at the beginning of month 1 , i.e., end of month 0 .) (a) Formulate a linear program to solve for the new optimal production plan. Make sure your variables are clearly defined, and that your objective and constraints are written out completely