High School

The cost of producing \( n \) bottles of wine in USD is represented by the cost function \( C(n) \), where \( C(n) = 5.2n + 73.6 \).

If a bottle of wine is sold for 8.15 USD, after selling how many bottles of wine does the company make a profit?

1) 25
2) 31
3) 20
4) 24

Answer :

Final answer:

The company will make a profit after selling 25 bottles of wine, as profit is achieved when revenue exceeds cost and, in this case, selling 25 bottles ensures that revenue is greater than the cost.

Explanation:

To determine after selling how many bottles of wine the company makes a profit, we first establish the revenue function, R(n), which is the amount obtained from selling n bottles of wine. Using the given price of 8.15 USD per bottle, R(n) = 8.15n. A profit is made when the revenue exceeds the cost, so we set R(n) > C(n) and solve for n:

R(n) = 8.15n > 5.2n + 73.6

Now, we simplify the inequality:

8.15n - 5.2n > 73.6

2.95n > 73.6

n > 73.6 / 2.95

n > 24.949

Since we can't sell a fraction of a bottle, the company needs to sell at least 25 bottles to make a profit.

Therefore, the company will start making a profit after selling 25 bottles of wine.

Learn more about Break-even Point here:

https://brainly.com/question/35967655

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