In July $2001,$ James H$.$ Miller, President of PPL Generation LLC$,$ had a decision to make. Pennsylvania Power & Light$$s power generation subsidiary, PPL Montana, had landed a $5-$year contract to supply $500$ megawatts of power capacity to Montana Power. Montana Power provided power to its $285,000$ customers but needed to buy capacity because in a strategic move it had recently sold its power generation capacity to other firms, including Pennsylvania Power & Light. Miller had three options for procuring the power to fulfill the contract: $1)$ PPL$$s hydro facilities in Montana $2)$ PPL$$s J$.$E$.$ Corette Plant, a coal$-$fired facility southwest on the Yellowstone River of Billings $3)$ Buy it from other generators in the spot market and resell it to Montana Power. Current spot market prices, for $5-$year contracts, were about $$44$ per megawatt hour, attractively below the $$50$ he was getting from Montana Power under the contract. But these spot prices were notoriously unstable, particularly because of the California power crisis. Should he lock in these profitable prices, and if so$,$ how much capacity should be buy? Miller asked Jennifer Y$.$ Rodriguez, his new staff economist, to prepare an analysis of the generation costs and called his staff together to give him recommendations. John Chamberlain, Miller$$s VP for customer relations, wondered out loud at the beginning of the meeting why there was even any question at all. Why would PPL want to buy power from other producers just to turn around and sell it again? He pointed out that, together, PPL$$s hydro facility and Corette plant had more than enough capacity to meet the $500-$megawatt contract, with some left over to sell onto the spot markets. PPL Montana$-$Hydro had $476-$megawatt capacity and the J$.$E$.$ Corette Plant had $227-$megawatt capacity. Because hydro generation tended to cost less, Chamberlain suggested using all $476$ from the hydro and $24$ from the Corette Plant, reserving the remaining capacity to sell onto spot markets when the prices were attractive. Rodriguez agreed that there was enough capacity internal to PPL$$s own generation facilities to cover the $500-$megawatt contract. But, she said she disagreed with Chamberlain on two points. She explained that through a regression analysis of recent historic cost information she gathered from the facility managers, she estimated the total generation cost structure of the hydro facilities and of the coal plant. Quadratic cost functions seemed to fit best. The current cost structure, she said, was: