Question

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)=___

Answer 1

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

$C(x)=a+bx,$

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

$C(30)=1000.$

Therefore:

$1000=100+b(30).$

Solving the above equation for b, we get:

$\begin{gathered} 1000-100=30b, \\ 900=30b, \\ b=\frac{900}{30}, \\ b=30. \end{gathered}$

Answer:

$C(x)=100+30x.$