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3. (*) A soft drinks firm buys fruit at the beginning of each month i at a cost per 100kg of p, in units of 1000. The firm can store up 2000kg of fruit at any given time but the cost in units 1000 of refrigeration per month per 100kg is ri. The consumption requirements are per month in 100kg units. Based on last year's figures the following estimates have been made: i Pi 18 Jan Feb Mar April May June July Aug Sept Oct Nov Dec 17 17 15 12 8 7 6 9 12 14 17 1 1 2 2 3 5 6 6 5 3 2 9 6 6 7 11 14 16 18 15 10 7 6 T' (a) Find the best purchasing schedule starting from January based on these estimates assuming that the firm has no fruit in storage on Jan 1st. How much will fruit cost for the year and how much will be spent on refrigeration? (b) Suppose that the firm has 500kg of fruit in storage at the beginning of the year. What is the best purchasing schedule that ensures that 500kg are again in storage at the very end of the year? 3. (*) A soft drinks firm buys fruit at the beginning of each month i at a cost per 100kg of p, in units of 1000. The firm can store up 2000kg of fruit at any given time but the cost in units 1000 of refrigeration per month per 100kg is ri. The consumption requirements are per month in 100kg units. Based on last year's figures the following estimates have been made: i Pi 18 Jan Feb Mar April May June July Aug Sept Oct Nov Dec 17 17 15 12 8 7 6 9 12 14 17 1 1 2 2 3 5 6 6 5 3 2 9 6 6 7 11 14 16 18 15 10 7 6 T' (a) Find the best purchasing schedule starting from January based on these estimates assuming that the firm has no fruit in storage on Jan 1st. How much will fruit cost for the year and how much will be spent on refrigeration? (b) Suppose that the firm has 500kg of fruit in storage at the beginning of the year. What is the best purchasing schedule that ensures that 500kg are again in storage at the very end of the year

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