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Math Statistics - Total Cost Function

by Amro
(Seattle, WA )










































Cost Function

A company finds that it costs a total of     to produce     units of a new product.

They also find that it costs a total of     to produce     units of the same product.

Use algebra to find a linear expression for the Total Cost Function, and type your algebraic expression below in terms of the variable .

(Use the Preview button to test the syntax of your expression before you submit your answer.)

Comments for Math Statistics - Total Cost Function

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Apr 15, 2013
Cost Function
by: Staff


Answer


Part I


The problem statement does not include the costs or the number of units produced.

Therefore, I have inserted the following variables for the missing numbers:

C: cost to produce W units of product

D: cost to produce Z units of product


With these variables inserted in the blank spots, the problem statement now reads:

A company finds that it costs a total of "C" to produce "W" units of a new product.

They also find that it costs a total of "D" to produce "Z" units of the same product.

Use algebra to find a linear expression for the Total Cost Function, and type your algebraic expression below in terms of the variable .

A linear equation has the form:
The slope intercept form of a linear equation is shown below

Generalized Slope Intercept Form of a Linear Equation




m = slope, the change in the y-value each time the x-value increases by 1

b = y-intercept, that y-value when x = 0. When a linear equation is graphed, b is that y-value where the graph crosses the y-axis.


applying this generalized format to the Total Cost Function


T: Total cost

b = T intercept. Equivalent to the y-intercept, b = fixed overhead

m = slope of the total cost function. This is the marginal cost (unit cost) of producing one unit of product.

X: number of units produced

Linear Cost Function:  quantifies the total cost of production for x units of product





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Apr 15, 2013
Cost Function
by: Staff


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Part II

Solving for the Total cost function.


W Units

C = mW + b

Production Cost to Produce W units





Z Units

D = mZ + b

Production Cost to Produce Z units




solve for m

Subtract the second equation from the first equation

Subtract the two equations




Factor out the slope, m

Factor out the slope, m





Divide each side of the equation by (W - Z)

Divide each side of the equation by (W - Z)





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Apr 15, 2013
Cost Function
by: Staff


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Part III


m is now a known value

At this point, the Cost Function looks like this:

Cost function with known value of the slope, m





Solve for the value of the slope-intercept b

Use the cost of "C" incurred to produce "W" units

Substitute "C" for "T" and "W" for "x"

Equation to calculate the fixed expense, b




To calculate the final value for "b", subtract [(C - D)/(W - Z)]*W from each side of the equation

Subtract from each side of the equation




Final answer:

Final Cost Function









Thanks for writing.

Staff
www.solving-math-problems.com



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