(a) To minimize the marginal cost, the derivative of the cost function C(x) must be set equal to zero and solved for x.
C'(x) = 10x - 200 = 0
x = 20
Therefore, 20 thousand cell phones should be manufactured to minimize the marginal cost.
(b) To find the minimum marginal cost, substitute x = 20 into the cost function C(x).
C(20) = 5(20)2 - 200(20) + 4000
C(20) = 4000 - 4000 + 4000
C(20) = 4000
Therefore, the minimum marginal cost is $4000.
83.
Minimizing Marginal Cost The marginal cost of a product can be thought of as the cost of producing one additional unit of output. For example, if the marginal cost of producing the 50th product is $6.20, it cost $6.20 to increase production from 49 to 50 units of output. Suppose the marginal cost C (in dollars) to produce x thousand mp3 players is given by the function
C(x) = x2 – 140x + 7400)
Minimizing Marginal Cost
(See Problem 83).
3.3 #84
The marginal cost C (in dollars) of manufacturing x cell phones (in thousands) is given by
C(x) = 5x2 – 200x + 4000.
(a) How many cell phones should be manufactured to minimize the marginal cost?
(b) What is the minimum marginal cost?
I have to answer the second (a,b) question but use the first as a reference.
1 answer
1 answer