The City of Regina is growing in population and the public works department projects the need for an

increased water supply. The current water supply is drawn from a reservoir on a local stream and is of

good quality, but future sources$-$the ones to be tapped next$-$have various problems. Water from a nearby

aquifer is available in adequate supply, but its hardness level is too high unless it is blended with a lower

hardness source. The total pounds of hardness per million gallons is limited to $1,200(143$ ppm in possibly

more familiar terms$)$ in the final blended supply. Water from a distant stream is of sufficient quality, but a

pipeline would have to be built to convey it$,$ and the cost to pump the water to the water treatment plant

is quite high. The City of Regina is conducting its planning in stages. The first stage is to plan for ten years from the

present. The three sources are: source $1-$ the current supply, source $2-$the aquifer, and source $3-$ the distant

stream. The costs to obtain water in dollars per million gallons, the supply limits in millions of gallons per

day, and the hardness in pounds per million gallons are given below. For example, if the present water

supply is developed further, up to $25$ million gallons per day $($mgd$)$ could be made available from source

$1$ at a cost of $$500$ per million gallons. Each additional million gallons from this source would contribute

$200$ pounds of hardness to the total water supply. A total of $150$ additional million gallons per day is needed

by the end of ten years.

Source $1$ Source $2$ Source $3$

Cost $($$$/$mgd$)50010002000$

Supply limit $($mgd$)25120100$

Hardness $($lb$/$mg$)2002300700$

The city council members are interested in a least$-$cost strategy for expanding the water supply, while

ensuring that the water supply remains of sufficient quality. Provide the optimal solution to the city council

members.