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Assume that the situation can be expressed as a linear cost function. Find the cost function.Fixed cost is $100; 30 items cost $1000 to produce.The linear cost function is C(x)=___

Respuesta :

Given that C(x) is a linear function, it can be expressed as:

[tex]C(x)=a+bx,[/tex]

where a, and b are constants.

Now, we are given that there is a fixed cost of 100, therefore, a=100. Now, we know that

[tex]C(30)=1000.[/tex]

Therefore:

[tex]1000=100+b(30).[/tex]

Solving the above equation for b, we get:

[tex]\begin{gathered} 1000-100=30b, \\ 900=30b, \\ b=\frac{900}{30}, \\ b=30. \end{gathered}[/tex]

Answer:

[tex]C(x)=100+30x.[/tex]

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