The revenue for selling a units of a product is R = 40x. The cost of producing x units is C = 20 + 7700.In order to obtain a profit, the revenue must be higher than the cost, so we want to know, for what values of a will this product return a profit.To obtain a profit, the number of units must be greater than _____

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AolaniH75485 AolaniH75485 · Answer 1 · 2022-10-26T11:36:23+02:00

EXPLANATION:

We are given the revenue function and the cost function for x units of a product as follows;

[tex]\begin{gathered} Revenue=40x \\ Cost=20x+7700 \end{gathered}[/tex]

We are also told that to obtain a profit, the revenue must be higher than the cost. This means;

[tex]\begin{gathered} Profit: \\ R(x)>C(x) \end{gathered}[/tex]

To determine which unit(s) of x will yield a profit, we can now substitute the values into the equation above;

[tex]\begin{gathered} Profit: \\ 40x>20x+7700 \end{gathered}[/tex][tex]\begin{gathered} Profit: \\ 40x-20x>7700 \end{gathered}[/tex]

[tex]\begin{gathered} Profit: \\ 20x>7700 \end{gathered}[/tex]

Divide both sides by 20;

[tex]\frac{20x}{20}>\frac{7700}{20}[/tex]

[tex]x>385[/tex]

For this answer, we know that to make a profit, the units produced must be greater than 385 units.

ANSWER:

To obtain a profit the number of units must be greater than 385