A number of power stations are committed to meeting the following electricity load demands over a day:[16]

12	[a.m.]	to	6	a.m.	15,000 megawatts
6	a.m.	to	9	a.m.	30,000 megawatts
9	a.m.	to	3	p.m.	25,000 megawatts
3	p.m.	to	6	p.m.	40,000 megawatts
6	p.m.	to	12	[a.m.]	27,000 megawatts

There are three types of generating unit available: 12 of type 1, 10 of type 2, and five of type 3. Each generator has to work between a minimum and a maximum level. There is an hourly cost of running each generator at minimum level. In addition there is an extra hourly cost for each megawatt at which a unit is operated above minimum level. To start up a generator also involves a cost. All this information is given in Table 15.1 (with costs in £).

In addition to meeting the estimated load demands there must be sufficient generators working at any time to make it possible to meet an increase in load of up to 15%. This increase would have to be accomplished by adjusting the output of generators already operating within their permitted limits.

Which generators should be working in which periods of the day to minimize total cost?

What is the marginal cost of production of electricity in each period of the day; i.e. what tariffs should be charged?

What would be the saving of lowering the 15% reserve output guarantee; i.e. what does this security of supply guarantee cost?