Respuesta :
Answer:
The linear cost function is [tex]C(x)=40\cdot x+2300[/tex]
Step-by-step explanation:
A linear cost function expresses cost as linear function of the number of items
[tex]C(x)=mx+b[/tex]
Here, C(x) is the total cost, and x is the number of items. The slope m is called the marginal cost and b is called the fixed cost.
From the information given we know
m = $40 and C(180) = $9500
We can find the value of b in this way
[tex]C(x)=mx+b\\C(180)=\$40\cdot 180+b=\$9500[/tex]
solving for b
[tex]b=\$9500-\$40\cdot 180=\$2300[/tex]
The linear cost function is [tex]C(x)=40\cdot x+2300[/tex]
The linear cost function is C(x) is [tex]\rm C(x) = 40x+2300[/tex]
Given
Marginal cost: $40; 180 items cost $9500 to produce.
What is the equation of the linear function?
The linear function is expressed as;
[tex]\rm y = mx+c[/tex]
A linear cost function expresses cost as a linear function of the number of items;
[tex]\rm C(x) = mx+b[/tex]
C(x) is the total cost, and x is the number of items.
The slope m is called the marginal cost and b is called the fixed cost.
The value of m is $40.
And the value of x is 180.
Substitute all the values in the equation;
[tex]\rm C(x) = mx+b\\\\C(180)=40\times 180 +b\\\\9500=7200+b\\\\b = 9500-7200\\\\b =2300[/tex]
Therefore,
The linear cost function is C(x) is;
[tex]\rm C(x) = 40x+2300[/tex]
Hence, the linear cost function is C(x) is [tex]\rm C(x) = 40x+2300[/tex].
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