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A commodities trading firm knows the prices at which it will be able to buy and cell a certain commodity during the next five months. The buying price c(i) and selling price p(i) (per kilogram of the commodity) for each of the given months (i) as follows. Month 2 3 1.00 0.50 0.60 0.60 ci) 1 0.50 n/a 4 0.70 0.40 5 n/a 0.60 pi) The firm's warehouse has a maximum capacity of 45000 kilograms. At the beginning of the first month the firm has 81000 available for the investment (to be used, in particular, for buying the commodity). The firm has also an opportunities to invest money in stocks. Opportunities to invest will be available at the beginning of first, second, third, and forth months. Each pound invested will return 1.05 one month later; the return can be immediately reinvested in any alternative. Assume that no storage costs are incurred and that sales are made at the beginning of the month, followed by purchases. What is the maximal profit (in pounds) the company can gain in this period of time (i.e. by the beginning of month five) using an optimal investment strategy