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=(900)/(30), \\ b=30. \end{gathered}`

Answer:

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