Powerco needs to determine a capacity expansion plan to meet Bloomington’s power needs for the next 20 years. The current capacity is 5000 kwh. The demand for the current year is 4000 kwh, and demand is expected to increase by 1000 kwh in each succeeding year. At the beginning of each year, Powerco must determine the amount of capacity to add, given the following inputs:

■ Any year in which capacity is added, a fixed cost of $120,000 is incurred plus a cost of $120 per kwh of capacity.

■ At most 10,000 kwh of capacity can be added in a single year.

■ It costs $25 per year to maintain a unit of capacity.

■ It costs $12 per year to produce a kwh.

■ If production does not meet demand, a shortage cost of $80 per kwh short is incurred.

Develop a linear integer model to help Powerco minimize its costs for the next 20 years.