The total cost (in dollars) of producing x college textbooks...

The total cost (in dollars) of producing x college textbooks is C(x) = 50x + 95,000. (a) What are the fixed costs? (b) What is the marginal cost per book? (c) What is the total cost of producing 1300 books? 36,000 books? (d) What is the average cost when 1300 books are produced? when 36,000 books are produced? (a) The fixed costs are $ \boxed{} (Simplify your answer.)

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00:01 Hello students, for fixed cost, fixed cost, the fixed cost are the cost that don't depend on the quantity of books produced.

00:13 In this case, the function c of x is equal to 40x plus 95000.

00:21 So the fixed cost are represented by constant term which is 95000.

00:27 So fixed cost, so fixed cost are 95000 dollar.

00:41 Now moving forward to the second bit, that is b bit, marginal cost per book.

00:52 So in this, the marginal cost per book, marginal cost is the additional cost incurred when producing one more unit and can be found by taking the derivative of the cost function with respect to x.

01:09 In this case, the derivative of c of x is c dash x is equal to 40.

01:16 So marginal cost, marginal cost per book is, cost per book is 40 dollar.

01:28 Now moving forward to the third bit, total cost per producing 800 books and 37000 books.

01:35 So to find the total cost producing a certain number of books, we can multiply, multiply substituting the value of x in the cost function.

01:45 So c of x is equal to 40x plus 95000.

01:50 So here we'll put x equal to 800.

01:54 So x equal to 800.

01:56 So c of 800 is equal to 40x800 plus 95000.

02:04 So here this is equal to 32000 plus 95000 equal to 127000 dollar for 37000 book...

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