Question

Calculus integration help needed..? See the attachment below. Thanks :)

Answer 1

I'll try BUT I am completely out of my turf here...

Explanation:

Observing the question I suspect that the Marginal Cost `MC=C'` should be the derivative, wrt `x` (representing the quantity), of the Total Cost `TC` function;

so that:

`MC(x)=(d(TC(x)))/(dx)`

so that, to find the Total Cost it should be necessary to integrate, i.e.:

`TC(x)=int(MC(x))dx`

or:

`TC(x)=int(-0.005x+4.50)dx`

giving:

`TC(x)=int(-0.005x)dx+int(4.50)dx=-0.005x^2/2+4.50x+C`

Now the bit I am not sure of: I think that the constant `C` represents the Fixed Costs that can set equal to zero; so we get for `x=250"lb"`:

`TC(250)=-0.005*(250)^2/2+4.50*(250)+color(red)(0)=968.75` dollars per pound.

I think....