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18 3. A company manufactures two products: premium apple juice and regular apple juice. Both products are made by combining the juice of two types

18 3. A company manufactures two products: premium apple juice and regular apple juice. Both products are made by combining the juice of two types of apples: grade 6 and grade 3. Each apple yields 50ml of apple juice, and the apple juice in premium juice and regular juice must have average grades of at least 5 and 4, respectively. During the next two weeks the company can sell up to 1200 litres of premium juice and up to 2500 litres of regular juice per week. Premium juice sells for R25 per litre, while regular juice sells for R16 per litre. At the beginning of week 1, the company has 100 kg grade 6 and 200 kg grade 3 apples in storage. The company can buy extra apples at a cost of R30/kg for grade 6 apples and R25/kg for grade 3 apples during period 1, and at a cost of R32/kg for grade 6 apples and R27/kg for grade 3 apples during period 2 (assume there are 10 apples in a kg). Juice spoils at the end of the week, so it makes no sense to make extra juice during week 1 in the hope of using it to meet week 2 demand. However, apples not used at the end of week 1 may be stored and used to produce juice in week 2 at a storage cost of R2.50/kg apples (any grade) per week. In addition to the cost of the apples, it costs R2 to produce each litre of apple juice (premium or regular). Formulate a Linear Program (LP) that can be used by the company to maximise profits over the next two weeks.

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