Your boss needs your help in figuring out the constraints so that she can complete an aggregate plan using linear programming. She sells the product for $50 per unit. She wants to minimize costs. She is forecasting demand for next year as:

Jan	1500
Feb	1700
Mar	1900
Apr	2100
May	2300
Jun	2500
Jul	2700
Aug	3100
Sep	2600
Oct	2300
Nov	1900
Dec	1700

Her costs are:

Materials (per unit)	$ 28
Inventory holding (per unit per month)	$ 6
Marginal cost of stockout (per unit per month)	$ 5
Hiring & training (per worker)	$ 150
Layoff (per worker)	$ 300
Regular time (per hour)	$ 15
Overtime (per hour)	$ 22
Subcontracting (per unit)	$ 30

Your boss knows this information about labor:

Beginning workforce	65
Working days in a month	20
Worker productive time (hours per day)	7
Maximum overtime (hours)	15
Labor hours required (per unit)	4

Finally, here is what your boss wants for inventory management:

Beginning	1500
Ending	500
Stockout at the end of June	0

Here are things your boss wants you to figure out:

1. Inventory for the period (It) is the beginning inventory minus the beginning stockout plus the production for the period (Pt) plus subcontracting for the period (Ct) which equals the demand for the period (Dt) plus the ending inventory (It) minus the ending stockout (St). How would you write the constraint for the demand for the period (Dt)?

Bonus question: What is the total revenue for the year?