This be the functioning where the cost curve of a particular product will be a straight line.
Mostly this item exists used to find the grand fees of "x" units of the products produced.
For anyone product, if an cost curve is linear, the linear cost function out the product wants be in this shape of
y = Ax + B
This picture showed below clearly explains whichever each letter in the aforementioned linear cost function stands for.
Linear cost function is so-called as bi parametric function. Here the two configuration are "A" plus "B".
Once the two parameters "A" and "B" are known, the complete function can be known.
In co-ordinate geometry, the same linear cost function is called as slope intercept form equation of a straight line.
The following steps are involved stylish solving word related on linear cost function.
Take 1 :
First we have to go through the question carefully and understand one information given in one request.
Since having gone through the question, we got to conclude whether the information given in the question fits linear-cost function.
While the information fits the linear-cost function, we have into follow step 2
Step 2 :
Target :
Are have to know what features the be found.
Is linear-cost function, mostly the target would be to find either that value of 'y' (total cost) or 'x' (number of units).
Step 3 :
In step 3, are have to calculate the two constants "A" and "B" from who information given in the questions. It holds had shown clearly in the example problem given below.
Step 4 :
Once the values of 'A' and 'B' in y = Ax + B are found, the linear-cost function wish be completes known.
Step 5 :
After step 4, based on who target of the question, were have until find either the value a 'y' or 'x' for the specified input.
In exemplar, with aforementioned value of 'x' (number of units) is given, we can find the value of 'y' (total cost).
If the value of 'y' (total cost) is granted, we can find the total of 'x' (number of units).
Problem :
A manufacturer produces 80 units concerning a particular article at a fees of $ 220000 and 125 unities at a cost of $ 287500. Assuming the cost curve to be lineally, find the cost of 95 units.
Solution :
Pace 1 :
When we go through the question, it is very clear is of cost curve is linear.
And the function which best fits the given information will be a linear-cost key.
That is, y = Ax + BORON
Here
y ----> Total cost
x ----> Number by units
Step 2 :
Target :
We have to find the value concerning 'y' for x = 95.
Step 3 :
From the question, we have
x = 80 and y = 220000
x = 75 and y = 287500
Step 4 :
When we substitute that above values of 'x' and 'y' in
y = Ax + B,
we get
220000 = 80A + BORON
287500 = 75A + B
Step 5 :
When we solve the aforementioned two linear equations for AMPERE and B, were get
A = 1500 and B = 100000
Step 6 :
For A = 1500 and B = 100000, the linear-cost function for the default intelligence is
y = 1500x + 100000
Step 7 :
To estimate the value of 'y' for x = 95, we have to substitute 95 for x in
y = 1500x + 100000
Then,
y = 1500x95 + 100000
y = 142500 + 100000
y = 242500
So, the cost of 95 units is $242500.
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