A manufacturer produces two types of fruit juice for filling and distributing, the X-S fruit juice and the Super fruit juice. A batch of X-S costs $375 to manufacture and a container of the Super costs $420. The manufacturer wishes to establish the weekly production plan that minimizes cost. Production of these products is limited to processing, testing and material. Each batch of X-S requires 4 hours processing whereas each batch of Super requires 2 hours of processing. Further each batch of X-S requires 4 hours of testing compared to 6 hours of testing for a batch of Super. A batch of X-S and a batch of Super each require 1 litre of material. Processing and testing have a maximum of 100 and 180 hours available respectively and the total material available is 40 litres. Because of a distribution agreement, the sales of X-S are limited to a weekly maximum of 20 batches and to honour an agreement with a loyal distributor, at least 10 batches of Super must be sold each week. By constructing and graphically solving an appropriate linear programming model, determine the optimum product mix of X-S and Super to minimize manufacturing costs.
A manufacturer produces two types of fruit juice for filling and distributing, the X-S fruit juice and the Super fruit juice. A batch of X-S costs $375 to manufacture and a container of the Super costs $420. The manufacturer wishes to establish the weekly production plan that minimizes cost. Production of these products is limited to processing, testing and material.
Each batch of X-S requires 4 hours processing whereas each batch of Super requires 2 hours of processing. Further each batch of X-S requires 4 hours of testing compared to 6 hours of testing for a batch of Super. A batch of X-S and a batch of Super each require 1 litre of material.
Processing and testing have a maximum of 100 and 180 hours available respectively and the total material available is 40 litres. Because of a distribution agreement, the sales of X-S are limited to a weekly maximum of 20 batches and to honour an agreement with a loyal distributor, at least 10 batches of Super must be sold each week.
By constructing and graphically solving an appropriate linear programming model, determine the optimum product mix of X-S and Super to minimize manufacturing costs.
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