Cost of Producing 101st Item | Solve C(x) Function

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In summary, the cost function for production of a commodity is C(x) = 369 + 21x - 0.08x^2 + 0.0006x^3. To find the actual cost of producing the 101st item, we need to input the value of 101 for x in the cost function. This will give us the cost of producing 101 items. However, if we want to find the cost of only the 101st item, we need to subtract the cost of producing 100 items from the cost of producing 101 items. This can be done by finding the cost function for producing 100 items, which is C(x) = 369 + 21x - 0
  • #1
invisiblewar
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The cost function for production of a commodity is given below.
C(x) = 369 + 21x - 0.08x^2 + 0.0006x^3

Find the actual cost of producing the 101st item. (Round the answer to the nearest cent.)

i know that
c'(x) = 21-.16x+.0018x^2

but for the life of me cannot figure out how to find the answer
 
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  • #2
How is "actual cost" defined?
 
  • #3
How much does it cost to produce 101 items?

How much does it cost to produce 100 items?

So what was the cost of that 101st item?

The derivative is irrelelvant here. This is purely and arithmetic problem.
 
  • #4
ive tried to just input the number and it keeps telling me that its the wrong answer I've done it every way i know how aghh
 
  • #5
ooo nevermind, i just got it...i feel dumb lol
 

What is the formula for calculating the cost of producing the 101st item?

The formula for calculating the cost of producing the 101st item is C(x) = FC + VC(x), where C(x) represents the total cost, FC is the fixed cost, and VC(x) is the variable cost per unit.

How do fixed costs and variable costs affect the cost of producing the 101st item?

Fixed costs, such as rent and equipment, remain constant regardless of the number of items produced. Variable costs, such as materials and labor, increase as the number of items produced increases. Therefore, the total cost of producing the 101st item will be higher due to the inclusion of both fixed and variable costs.

What factors can impact the cost of producing the 101st item?

Several factors can impact the cost of producing the 101st item, including changes in the cost of materials, labor, and overhead expenses. Inflation, production efficiency, and market demand can also affect the cost of producing the 101st item.

How does the cost of producing the 101st item compare to the cost of producing the 100th item?

The cost of producing the 101st item will likely be higher than the cost of producing the 100th item due to the inclusion of additional fixed and variable costs. However, the exact difference will depend on the specific circumstances and factors mentioned earlier.

How can the "C(x) function" be used to optimize the cost of producing the 101st item?

The "C(x) function" can be used to analyze the relationship between the cost of producing items and the number of items produced. By finding the point where the function reaches its minimum, the optimal number of items to produce can be determined, thus optimizing the cost of producing the 101st item.

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