A factory produces two products X and Y each of which must pass through two production processes A and B. Product X requires 10 hours in A and 8 in B, while product Y requires 10 hours in A and 3 in B. the maximum capacity of process A for a certain period is 1200hours and due to the cost and manpower agreements, process B must be used at least 4800hours over the same period. Due to fixed commitments, at least 600 Y products must be produced, while a maximum of 500 X products will be produced over the given period. i. Formulate the constraints for the above problem ii. If X has a contribution of Kshs. 100 and Y Kshs. 140, find the points that maximize and minimize total contribution and give the value of these contributions

a) Highlight four management applications of linear programming

b) A factory produces two products X and Y each of which must pass through two production processes A and B. Product X requires 10 hours in A and 8 in B, while product Y requires 10 hours in A and 3 in B. the maximum capacity of process A for a certain period is 1200hours and due to the cost and manpower agreements, process B must be used at least 4800hours over the same period. Due to fixed commitments, at least 600 Y products must be produced, while a maximum of 500 X products will be produced over the given period.
i. Formulate the constraints for the above problem
ii. If X has a contribution of Kshs. 100 and Y Kshs. 140, find the points that maximize and minimize total contribution and give the value of these contributions.
(11 marks)

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