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THE Cost function of a manufacturer is given C= 0.5x^3 - 5x^2 15x. Find the value of x at which slope of AC is minimum?
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THE Cost function of a manufacturer is given C= 0.5x^3 - 5x^2 15x. Fi...
Introduction:
In this problem, we are given a cost function of a manufacturer, and we are asked to find the value of x at which the slope of the average cost (AC) is minimum.
Calculating the Average Cost (AC):
The average cost is calculated by dividing the total cost (TC) by the quantity produced (x). Mathematically, AC = TC/x. To find the TC, we take the derivative of the given cost function.
Deriving the Total Cost (TC):
C = 0.5x^3 - 5x^2 + 15x
TC = C(x) = 0.5x^3 - 5x^2 + 15x
Deriving the Average Cost (AC):
AC = TC/x
AC = (0.5x^3 - 5x^2 + 15x)/x
AC = 0.5x^2 - 5x + 15
Calculating the Slope of AC:
To find the slope of AC, we take the derivative of the average cost function.
Deriving the Slope of AC:
d(AC)/dx = d/dx(0.5x^2 - 5x + 15)
d(AC)/dx = x - 5
Locating the Minimum Slope of AC:
To locate the minimum slope of AC, we set the derivative equal to zero and solve for x.
x - 5 = 0
x = 5
Conclusion:
Therefore, the value of x at which the slope of AC is minimum is 5. This means that the manufacturer should produce 5 units of the product to minimize the slope of the average cost function.
In this problem, we are given a cost function of a manufacturer, and we are asked to find the value of x at which the slope of the average cost (AC) is minimum.
Calculating the Average Cost (AC):
The average cost is calculated by dividing the total cost (TC) by the quantity produced (x). Mathematically, AC = TC/x. To find the TC, we take the derivative of the given cost function.
Deriving the Total Cost (TC):
C = 0.5x^3 - 5x^2 + 15x
TC = C(x) = 0.5x^3 - 5x^2 + 15x
Deriving the Average Cost (AC):
AC = TC/x
AC = (0.5x^3 - 5x^2 + 15x)/x
AC = 0.5x^2 - 5x + 15
Calculating the Slope of AC:
To find the slope of AC, we take the derivative of the average cost function.
Deriving the Slope of AC:
d(AC)/dx = d/dx(0.5x^2 - 5x + 15)
d(AC)/dx = x - 5
Locating the Minimum Slope of AC:
To locate the minimum slope of AC, we set the derivative equal to zero and solve for x.
x - 5 = 0
x = 5
Conclusion:
Therefore, the value of x at which the slope of AC is minimum is 5. This means that the manufacturer should produce 5 units of the product to minimize the slope of the average cost function.
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THE Cost function of a manufacturer is given C= 0.5x^3 - 5x^2 15x. Fi...
THE Cost function of a manufacturer is given C= 0.5x^3 - 5x^2 15x. Find the value of x at which slope of AC is minimum?
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THE Cost function of a manufacturer is given C= 0.5x^3 - 5x^2 15x. Find the value of x at which slope of AC is minimum?
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THE Cost function of a manufacturer is given C= 0.5x^3 - 5x^2 15x. Find the value of x at which slope of AC is minimum? for B Com 2024 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about THE Cost function of a manufacturer is given C= 0.5x^3 - 5x^2 15x. Find the value of x at which slope of AC is minimum? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for THE Cost function of a manufacturer is given C= 0.5x^3 - 5x^2 15x. Find the value of x at which slope of AC is minimum?.
THE Cost function of a manufacturer is given C= 0.5x^3 - 5x^2 15x. Find the value of x at which slope of AC is minimum? for B Com 2024 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about THE Cost function of a manufacturer is given C= 0.5x^3 - 5x^2 15x. Find the value of x at which slope of AC is minimum? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for THE Cost function of a manufacturer is given C= 0.5x^3 - 5x^2 15x. Find the value of x at which slope of AC is minimum?.
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