Assume that the production cost curve of a power generating unit may be represented by piecewise linear curves as:
Where P is the amount of power generated by the unit. Assume that the unit has a start-up cost of $1,000 and that it is initially shut down. The hourly electricity prices for a certain market, where this units bids into, are shown below.
Period 1 2 3 4 5 6 7 8
Price ($) 9.75 13.2 10.6 12 12.7 9.2 9.5 10
(a) Determine the hourly schedule of the unit to maximize its operational profit.
(b) Determine the total profit for each hour.