(This question has little to do with optimization; it's just about the electric power industry). Visit
http://www.midwestiso.org/page/LMP+Contour+Map+%26+Data and look up the 5-minute real-time "LMP" (Locational Marginal Price) at the location DECO.MONROE3 I think that's the large coal-fired power plant in Monroe, MI. The LMP is essentially the Lagrange multiplier for a large NLP; it is also the wholesale price of electricity at that point. I believe the units are $/MWh.
Report the value you find, and the date/time you looked. Also, convert it to cents per kWh. The retail price for electricity (including distribution charges, taxes, etc.) is around 11 cents per kWh, just for comparison.
Also, consider buying an 20-pack of AA batteries for $10.86 (I got the price from walmart.com). Each AA battery contains, let's say, 2500 milli-Amp-hours, which when multiplied by 1.5 volts gives 3.75 Watt-hours.
How much are you paying per kWh?
On 4:28pm 18-Nov (Eastern Time) I found a value of 24.18 $/MWh in the 5-minute real-time "LMP" (Locational Marginal Price)
at the location DECO.MONROE
That is ...
A cost comparison of AA batteries with utility power using the relationship between volts, amps, and watts is provided in the solution.