The MorTex Company assembles garments entirely by hand even though a textile machine exists which can assemble garments faster than a human can. Workers cost $50 per day, and each additional laborer can produce 200 more units per day (the same for each additional worker). Installation of the first textile machine on the assembly line will increase output by 1,800 units daily. Currently the firm assembles 5,400 units per day without the machine.
a. The financial analysis department at MorTex estimates that the price of a textile machine is $600 per day. Can management reduce the cost of assembling 5,400 units per day by purchasing a textile machine and using less labor? Why or why not?
b. The Textile Workers of Texas is planning to strike for higher wages. Management predicts that, if the strike is successful, the cost of labor will increase to $100 per day. If the strike is successful, how would this affect the decision in question above to purchase the textile machine. Explain.
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What are the 3 major differences between manufacturing in industry and manufacturing in the classroom?
a. To determine whether management can reduce the cost of assembling 5,400 units per day by purchasing a textile machine and using less labor, we need to compare the cost of labor with and without the machine.
Without the machine:
Labor cost = Number of workers * Cost per worker per day
The current output of 5,400 units per day requires a certain number of workers. Let's call this number "W".
With the machine:
Labor cost = Number of workers * Cost per worker per day + Cost of machine per day
The machine increases the output by 1,800 units per day, which means that the number of workers required will decrease by a certain number. Let's call this number "X".
To determine whether purchasing the machine reduces the cost, we need to compare the total cost of labor and machine without the machine (5,400 units per day) and with the machine (5,400 + 1,800 units per day).
Without the machine:
Total labor cost = W * $50 per day
With the machine:
Total labor cost = (W - X) * $50 per day + $600 per day
If the total labor cost with the machine is lower than the total labor cost without the machine, then management can reduce the cost of assembling 5,400 units per day by purchasing the textile machine.
b. If the cost of labor increases to $100 per day due to a successful strike by the Textile Workers of Texas, it would affect the decision to purchase the textile machine.
Without the machine:
Total labor cost = W * $50 per day
With the machine:
Total labor cost = (W - X) * $100 per day + $600 per day
If the strike is successful and the cost of labor increases to $100 per day, the total labor cost without the machine will be higher than the total labor cost with the machine. In this case, purchasing the machine would become even more cost-effective, as it reduces the number of workers required and therefore the labor cost.
Therefore, if the strike is successful and the cost of labor increases to $100 per day, it would strengthen the decision to purchase the textile machine.