Answered

The function C(x) = 10x +3,000 represents the cost to produce a number of items. How many items should beproduced so that the average cost is less than $30?Provide your answer



Answer :

Given:

The cost function is C(x) = 10x + 3000.

Explanation:

The equation for the average cost is,

[tex]\begin{gathered} A(x)=\frac{C(x)}{x} \\ =\frac{10x+3000}{x} \end{gathered}[/tex]

The inequality for x is,

[tex]\frac{10x+3000}{x}<30[/tex]

Solve the inequality for x.

[tex]\begin{gathered} \frac{10x+3000}{x}\cdot x<30\cdot x \\ 10x+3000-10x<30x-10 \\ \frac{3000}{20}<\frac{20x}{20} \\ 150So the number of items should be more than 150.

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