The Lake Lucky dam7 retains water in the reservoir lake of the same name to prevent flooding downstream and to assure a steady year-round supply of water for wildlife and nearby cities. The best available projections call for inflows it (cubic meters of water) to arrive at the reservoir on upcoming days t = 1,

c, 120. A minimum of at least r must be released through the dam every day to maintain downstream water quality, but the daily release can go as high as rQ. The current storage in the reservoir is s0 cubic meters, and storage levels must be kept between minimum and maximum limits s and sQ throughout the 120-

day period. Reservoir managers seek a 120-day plan that releases, as close as possible to target, R cubic meters each day and maintains a target level of S cubic meters stored in the reservoir. Both below- and above-target outcomes are considered equally bad, and release deviations are weighted equally with those for storage. Formulate a goal LP to compute a reservoir operating plan. Assume that no water is lost (i.e., all water that enters the reservoir eventually flows over the dam).