Question

The cost (in dollars) of producing x units of a certain commodity is C(x) = 9000 + 6x + 0.05x2. (a) Find the average rate of change of C with respect to x when the production level is changed from x = 100 to the given value. (Round your answers to the nearest cent.) (i) x = 102

Answer 1

Answer: 16

Explanation: Average rate of change of C with respect to X is given as

= $\frac{\Delta C}{\Delta X}$

= $\frac{(C(102)-C(100))}{(X(102)-X(100))}$

= $\frac{ 10132.2-10100}{102-100}$

= 32/2

= 16

Answer 2

Answer: The correct answer is $16.1 per unit.

Explanation:

C(x) = 9000 + 6x + 0.05x²

C(100) = 9000 + 6 × 100 + 0.05(100)²

           = 9000 + 600 + 500

            = 10,100

C(102) = 9000 + 6 × 102 + 0.05(102)²

           = 9000 + 612 + 520.5

            = 10,132.2

Now, the average rate of change of C with respect to x when production level changed from x = 100 to x = 102 is :

⇒ ${ \frac{C(102) - C(100)}{(102 - 100)} \\= \frac{10132.2 - 10100}{2}$

= $\frac{32.2}{2}$

= $16.1 per unit