A product is assembled from three parts that can be manufactured on two machines

Question

A product is assembled from three parts that can be manufactured on two machines A and B. Neither machine can process different parts at the same time. The number of parts processed by each machine per hour are summarized below:

Management seeks a daily schedule (for 8 hrs/day) of the machines so that the number of assemblies is maximized. Currently the company has three machines of type A and five machines of type B. Solve the problem. If only one machine can be acquired, which type would you recom- mend and why? Management is contemplating the purchase of a type A machine at a cost of $100,000. Suppose that the life of the machine is 10 years and that each year is equivalent to 2000 working hours. Would you recommend the purchase if the unit profit from each assembly is $ 1 ? Why or why not?

Explanation / Answer

Machine A Machine B Part1 10 8 Part2 16 12 Part3 25 Since each machine can process each part at one time then for 2000 hours available for machine A No of products can be produced would be considering 8 hours for each product to assemble Therefore 1 day = 8 hours = 1 hour = 10 product = 8 hour = 80 product= $80 Since the part A is 10 and part2 is 16 from machine A the wastage is less but whereas from machine B the actual production can be only 8 product in 1 hour and wastage would be more Thereofore 1 hour = 10 product 2000 = 20000 products = $20000 each year Since each year they an each 20000 therefore 10 years 200000 hence they should purchase machine A

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