You've been hired by a candle factory. The candle factory produces boxes of scented candles; they sell these boxes for $r each. It has done extensive research, and determined that for the next n weeks, the demand for candles will be d; boxes (i = 1,2,..., n). Due to fluctuating wax prices, the cost for producing a box of candles in week i is $pi. The candle factory can store an unlimited amount of boxes of candles for an unlimited amount of time; however, storing a box of candles costs $s per week (for example, storing a box of candles produced in week 5 and sold in week 7 incurs a cost of $2s). (a) Management wants to maximize profit. Formulate a Linear Program to solve the factory's problem; you may assume that the factory can produce fractional boxes of candles. (b) Because access to the factory's storage space is inconveniently situated, the number of stored boxes of candles can fluctuate by at most D per week. For example, if by the end of week 5 fifty boxes of candles are stored, then by the end of week 6 the number of boxes in storage must be at least 50 D and at most 50 + D. Adapt your formulation in part (a) to accommodate this additional requirement.