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.
For $600 the machine can produce 1800 units or 600/1800 = .333 per unit. For $50 the marginal worker can produce 200 units or 50/200 = .25 per unit. Which is the most cost effective?
Take it from here.
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To determine whether MorTex Company 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 costs of the two options: continuing with manual labor and purchasing the machine.
a. Cost analysis without the textile machine:
Currently, the firm assembles 5,400 units per day without the machine. Each worker costs $50 per day, and each additional laborer can produce 200 more units per day. Therefore, the current labor cost is:
(Number of laborers × Cost per laborer) = (Total units produced ÷ Additional units per laborer) × Cost per laborer
Using the given information:
Number of laborers = 0 (since no additional laborers are mentioned)
Cost per laborer = $50
Total units produced = 5,400 units
Additional units per laborer = 200 units
Substituting these values into the equation:
(0 × $50) = (5,400 ÷ 200) × $50 = $0
So, the current labor cost is $0 per day.
b. Cost analysis with the textile machine:
Installing the first textile machine on the assembly line will increase the output by 1,800 units daily. The price of the textile machine is $600 per day according to the financial analysis department.
To calculate the total cost with the textile machine, we need to consider the cost of labor and the cost of the machine.
Cost of labor:
Number of laborers = (Total units produced ÷ Additional units per laborer)
Using the given information:
Total units produced = 5,400 units
Additional units per laborer = 200 units
Substituting these values into the equation:
Number of laborers = (5,400 ÷ 200) = 27 laborers
Since each worker costs $50 per day, the labor cost will be:
Number of laborers × Cost per laborer = 27 × $50 = $1,350 per day.
Cost of the machine:
The price of the textile machine is $600 per day.
Total cost with the textile machine:
Labor cost + Machine cost = $1,350 + $600 = $1,950 per day.
Comparing the costs:
Without the textile machine: $0 per day.
With the textile machine: $1,950 per day.
Conclusion:
Since the cost of labor without the textile machine is $0 per day and the cost of using the textile machine and reducing labor is much higher at $1,950 per day, purchasing the textile machine will not reduce the cost of assembling 5,400 units per day.
b. If the cost of labor increases to $100 per day due to a successful strike, we need to recalculate the costs with the textile machine:
New labor cost:
Number of laborers × Cost per laborer = (Total units produced ÷ Additional units per laborer) × Cost per laborer
Number of laborers = (5,400 ÷ 200) = 27 laborers
Cost per laborer = $100
New labor cost = 27 × $100 = $2,700 per day.
Total cost with the textile machine:
New labor cost + Machine cost = $2,700 + $600 = $3,300 per day.
Comparison of costs:
Without the textile machine: $0 per day.
With the textile machine: $3,300 per day.
Conclusion:
Even with the increased labor cost of $100 per day, purchasing the textile machine would still not be financially beneficial. The cost of using the machine is significantly higher than the cost of manual labor. Therefore, it is not advisable to purchase the machine in this scenario.