A steel plant has two sources of ore, source a and source b. In order to keep the plant running, at least three tons of ore must be processed each day. Ore from source a costs $20 per ton to process, and ore from source b costs $10 per ton to process. Costs must be kept to no more than $80 per day. Moreover, federal regulations require that the amount of ore from source b cannot exceed twice the amount of ore from source a. If ore from source a yields 300 lbs of steel per ton, and ore from source b yields 400 lbs of steel per ton, how many tons of ore from each source should be processed each day to maximize the amount of steel produced?.