The cost C (in dollars) for producing x units of an item is given by C=370+2.55sqrtX. find the marginal cost when the production level is X=400 units.
My answer came out to 51/800, or .06375.
I'm not sure if I did it correctly.
C=370+2.55 sqrt x
c'=2.55/2 * 1/sqrt x
c'=1.275/sqrt400=1.275/20= you are correct
The cost C (in dollars) of producing x units of a product is given by C=3.6√x+500
Find the marginal cost when x=9.
Find the additional cost when the production increases from 9 to 10 units.
To find the marginal cost, we need to take the derivative of the given cost equation with respect to x.
Given: C = 370 + 2.55√x
Now, let's differentiate both sides of the equation with respect to x:
dC/dx = 0 + 2.55 * (1/2) * x^(-1/2)
Simplifying:
dC/dx = 2.55/(2√x)
= 1.275/√x
To find the marginal cost at production level x = 400 units, substitute this value into the derivative equation:
dC/dx = 1.275/√400
= 1.275/20
= 0.06375
Therefore, the marginal cost when the production level is X = 400 units is 0.06375 or $0.06375.
So, your answer of 51/800 or 0.06375 is correct.
To find the marginal cost when the production level is X=400 units, we need to find the derivative of the cost function with respect to X.
Given the cost function C = 370 + 2.55√X, we can find the derivative of C with respect to X as follows:
dC/dX = 0 + 2.55 * (1/2) * X^(-1/2) [using the power rule of differentiation]
= 2.55 * (1/2) * X^(-1/2)
= 1.275 * X^(-1/2)
Now, to find the marginal cost when X = 400 units, we substitute this value of X into the derivative equation:
dC/dX = 1.275 * 400^(-1/2)
= 1.275 * √(1/400)
= 1.275/20
= 0.06375
Therefore, the marginal cost when the production level is X=400 units is 0.06375 dollars.
Your answer is indeed correct. The marginal cost indicates the rate at which the cost changes as the production level increases by one unit. In this case, the marginal cost is approximately $0.06375 per unit.