Question

. It costs C(x) = $\sqrt{x}$ dollars to produce x golf balls. What is the marginal production cost to make a golf ball? What is the marginal production cost when x = 25? when x= 100? (Include
units.)

Answer 1

The marginal cost when x = 25 and when x = 100 are $0.1 and $0.05 respectively.

What is a Marginal Production Cost?

A marginal production cost is a derivative of a cost function. From the information given, the total cost is:

• C(x) = $\mathbf{\sqrt{x}}$

The marginal production cost can be expressed as:

$\mathbf{C'(x) = \dfrac{d}{dx}(\sqrt{x})}$

$\mathbf{C'(x) = \dfrac{1}{2\sqrt{x}}}$

However, when the cost is 25, the marginal production is:

$\mathbf{C'(25) = \dfrac{1}{2\sqrt{25} }}$

$\mathbf{C'(25) = \dfrac{1}{2\times5}}$

$\mathbf{C'(25) = \dfrac{1}{10}}$

C' (25) = $0.1

Also, when the cost is 100, the marginal production is:

$\mathbf{C'(100) = \dfrac{1}{2\sqrt{100} }}$

$\mathbf{C'(100) = \dfrac{1}{2\times10}}$

$\mathbf{C'(100) = \dfrac{1}{20}}$

C' (100) = $0.05

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