(a)

The function is .

Marginal cost function is the derivative of cost function.

Consider .

Differentiate on each side with respect to .

The marginal cost function is .

(b)

The marginal cost function is .

Substitute  in .

The marginal cost at the production level of  is $ /yard.

 means the incremental cost of producing one more yard after producing 

yards of fabric.

cost of producing 201^st  yard is about $32.

(c)

The actual cost to  produce the 201^st item is .

.

Find :

The actual cost of producing the 201^st item is $ .

We have .

is almost same as the cost of producing the 201^st item.

(a) .

(b) $ /yard ;  means the cost of producing 201^st yard.

(c) $ .