A utility company needs to meet an hourly demand for electricity (in MWh) over each day. It can generate power from oil, coal, nuclear and hydro-electric sources. Cost per MWh for oil, coal and nuclear are respectively 80, 40 and 10. Hydro-electric energy is free but there is only sufficient daily MWh energy available to meet 30% of the daily MWh demand. Given the hourly electricity proce of i, what is the optimal mix of sources for meeting the daily demand?

hours 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Demand 16057 15516 15185 14940 14802 14880 14998 15463 15612 16269 16471 16941 17360 17579 18071 18377 18466 18678 18745 18564 18694 18365 17514 16885 Lambdas 19.16 13.66 14.34 18.69 14.37 13.68 6.89 10.35 10.51 17.32 37.12 20.51 21.2 19.41 19.73 19.49 21.11 24.18 21.94 20.13 21.62 22.83 18.07 16.96