The cost function for production of a commodity is C ( x ) = 301 + 22 x 0.06 x 2

Question

The cost function for production of a commodity is

C(x) = 301 + 22x 0.06x2 + 0.0009x3.

C'(100).

This is the rate at which costs are increasing with respect to the production level when x = 100.This is the rate at which the production level is decreasing with respect to the cost when x = 100.    This is the cost of making 100 items.This is the amount of time, in minutes, it takes to produce 100 items.This is the number of items that must be produced before the costs reach 100.

(b) Find the actual cost of producing the 101st item. (Round your answer to the nearest cent.)

Explanation / Answer

a)

C(x) = 301 + 22x 0.06x^2 + 0.0009x^3

Find the derivative using power rule as

C'(x) = 0 +22 -0.12x +0.0027x²

C'(x) = 0.0027x²-0.12x +22

Plug in x=100

C'(100) = 0.0027*100^2-0.12(100) +22

=37

Thus, C'(100) is 37

----------------

This is the rate at which costs are increasing with respect to the production level when x = 100

-------------------

b)

actual cost of producing the 101st item =C(101)-C(100)

=2838.21-2801

=$37.21

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.