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Problem 1 Multi-Period Water Planning. A Californian water company is preparing for the warmer months of the year when water becomes more difficult to come by. There are two sources of water available: they pump some water from their own aquifer and buy the remaining water from out of state. The demand remains at a constant 75 thousand gallons per month, but their aquifer produces less and less each month. They own storage tanks capable of holding 100 thousand gallons of water at any given time; it already contains 30 thousand gallons. Both the projected cost of buying water from out of state and the amount of water that can safely be extracted from the aquifer is given in the table below. Let xi indicate the amount of water to be purchased in month i and si represent the amount of water to be stored in month i for use in month i+1. We seek to minimize the cost of buying enough water to meet demand each month. Formulate this problem as a Linear Program and solve it using Excel-solver. Report both your LP and its optimal solution in your submission