# 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 .

### Comments for Math Statistics - Total Cost Function

 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 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 ---------------------------------------------------------

 Apr 15, 2013 Cost Function by: Staff --------------------------------------------------------- Part II Solving for the Total cost function. W Units C = mW + b Z Units D = mZ + b solve for m Subtract the second equation from the first equation Factor out the slope, m Divide each side of the equation by (W - Z) ---------------------------------------------------------

 Apr 15, 2013 Cost Function by: Staff --------------------------------------------------------- Part III m is now a known value At this point, the Cost Function looks like this: 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" To calculate the final value for "b", subtract [(C - D)/(W - Z)]*W from each side of the equation Final answer: Thanks for writing. Staff www.solving-math-problems.com