A product is assembled from three parts that can be manufactured on two machines
ID: 3770948 • Letter: A
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:
Machine A Machine B
Part 1 10 8
Part 2 16 12
Part 3 - 25
Managment 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 of type B.
a) Solve the problem
b) If only one machine can be aquired, which type would you recomend and why?
c) 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 the each year is equivalanet to 2000 working hours. Would you recommend the purchase if the unit profit from each assembly is $1? Why or why not?
Explanation / Answer
Number of Part 1 produced in each day (each machine) = 8 * 10 = 80
Number of Part 2 produced in each day (each machine) = 8 * 16 = 128
Number of Part 1 produced in each day (using 3 machines) = 80 * 3 = 240
Number of Part 2 produced in each day (using 3 machines) = 128 * 3 = 384
Number of available machines of type B = 5
Number of Part 1 produced in each day (each machine) = 8 * 8 = 64
Number of Part 2 produced in each day (each machine) = 8 * 12 = 96
Number of Part 3 produced in each day (each machine) = 8 * 25 = 200
Number of Part 1 produced in each day (using 3 machines) = 64 * 5 = 320
Number of Part 2 produced in each day (using 3 machines) = 96 * 5 = 480
Number of Part 3 produced in each day (using 3 machines) = 200 * 5 = 1,000
Total Number of products of Part 1 = 240 + 320 = 560
Total Number of products of Part 2 = 384 + 480 = 864
Total Number of products of Part 3 = 1,000 = 1,000
Total number of Assembled products per day = 560
To maximize the Assembled products per day, need to produce more Part 1 of Product such that our profit become maximum.
Life of the machine A = 10 years.
Working hours (Each year) = 2000 hours.
Number of available machines of type A = 3
Number of Part 1 produced in each year (each machine) = 2000 * 10 = 20,000
Number of Part 2 produced in each year (each machine) = 2000 * 16 = 32,000
Number of Part 1 produced in each year (using 3 machines) = 20,000 * 3 = 60,000
Number of Part 2 produced in each year (using 3 machines) = 32,000 * 3 = 96,000
Number of available machines of type B = 5
Number of Part 1 produced in each year (each machine) = 2000 * 8 = 16,000
Number of Part 2 produced in each year (each machine) = 2000 * 12 = 24,000
Number of Part 3 produced in each year (each machine) = 2000 * 25 = 50,000
Number of Part 1 produced in each year (using 3 machines) = 16,000 * 5 = 80,000
Number of Part 2 produced in each year (using 3 machines) = 24,000 * 5 = 120,000
Number of Part 3 produced in each year (using 3 machines) = 50,000 * 5 = 250,000
Total Number of products of Part 1 = 60,000+80,000 = 140,000
Total Number of products of Part 2 = 96,000+1,20,000 = 216,000
Total Number of products of Part 3 = 250,000 = 250,000
To increase the assembled products, we should purchase Machine A. Without purchasing new Machine A number of assembled products each year are: 140,000.
Profit earned is $140,000.
Now there are part2 and part 3 are also manufactured, but they are as a waste because without part1 a product can’t be manufactured. To maximize the number of assembled products, purchase machine A.
After purchasing,
Total Number of products of Part 1 = 140,000 + 20,000 = 160,000
Total Number of products of Part 2 = 216,000 + 32,000 = 248,000
Total Number of products of Part 3 = 250,000
Now assembled products are 160,000.
Profit earned is $160,000(each year)
Profit earned by new Machine A (each year) = 160,000-140,000 = $20,000
Profit earned by new Machine A (in 10 years) = 20,000 * 10 = 200,000 $
Cost of new machine = 100,000 $.
Here profit is double from the cost of Machine A. Thus, Machine A is to be purchased to maximize the profit.
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