Question

6. In deciding whether to set up a new manufacturing plant, company analysts have established that a reasonable function for the total cost to produce x items is C(x) = 500,000 + 4.75x. (a) Find the total cost to produce 100,000 items. (b) Find the marginal cost of the items to be produced in this plant.

Answer 1

`\begin{gathered} a)\$975,000 \\ b)\$4.75_{} \end{gathered}`

1)

a) Let's find out the total Cost to Produce 100,00 items considering x to stand for "items", so we can write out:

`\begin{gathered} C(x)=500,000+4.75x \\ C(100,000)=500,000+4.75(100,000) \\ C(100,000)=\$975,000 \end{gathered}`

Note that we just had to plug into x, the number of items.

b) The Marginal Cost

On the other hand, the Marginal Cost can be found by taking the first derivative of the Total Cost function, so we can write out:

`\begin{gathered} C(x)=500,000+4.75x \\ C^(\prime)(x)=4.75 \end{gathered}`

The basic idea of the marginal cost is the cost per unit $4.75

3) Hence, the answer is:

a) $975,000

b) $4.75 per unit