A Company manufactures two product ( X and Y ) and the profit per unit sold is $ 10 and $ 5 respectively . Each product has to be assembled on a particular machine , each unit of product X taking 12 minutes of assembly time and each unit of product Y 25 minutes of assembly time . The company estimates that the machine used for assembly has an effective working week of only 30 hours ( due to maintenance / breakdown ) . Technological constraints mean that for every five units of product X produced at least two units of product Y must be produced .
a. Formulate the problem of how much of each product to produce as linear program !
b. Solve this linear program graphically !
c. The company has been offer the chance to hire an extra machine , thereby doubling the effective assembly time available . What is the maximum amount you would be prepared to pay ( per week ) for the hire of this machine and why ?

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