Pregunta
Write a cost function for the problem. Assume that the relationship is linear.
Fixed cost,
A.
B.
C.
D.
Fixed cost,
A.
B.
C.
D.
Ask by Rodriquez Barker. in the United States
Mar 20,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The cost function is
Solución
Let the cost function be linear, so we have
where
Given that producing 5 items costs
Subtract the fixed cost to find the total variable cost for 5 items:
Now, solve for
Thus, the cost function is:
The correct answer is Option C.
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Simplifique esta solución Extra Insights
To determine the correct cost function, let’s break down the information:
- The total cost can be expressed as
. - Given that the fixed cost is
, we can write part of the equation as . - The cost for producing 5 items is given as
. So we can set up the equation: . - Simplifying,
, which gives us a variable cost of per item.
Thus, the cost function becomes
Now, let’s explore the historical context surrounding linear cost functions. Linear cost functions have their roots in the industrial revolution, where manufacturing processes started to evolve. As factories gained efficiency, understanding costs became paramount, leading to simplified models to predict expenses based on production volume.
For real-world application, knowing how to define a cost function is crucial for businesses. Companies can use it to forecast budgets, set prices, or determine break-even points. Understanding your costs helps in making informed decisions that can significantly impact profit margins and overall financial health.
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