# Maximize Profit: Solve Revenue Problem for G-Food Catering

• joejo
In summary: the derivative is just like the slope of a line, and when u set it equal to 0, it means that the line goes straight down...so in this case, if we set the derivative of (3- 0.25n)(100+ 10n) to 0, then we get that n= 50. so 50 lunches will be sold.
joejo
have final answer...cant figure out how to do it...i usually post my answers..but for this one I've been spending the past 2 days on it and not matching it with the correct answer in the textbook can someone please help me out as I am homeschooling and have no teacher to ask...

thanks in advance!

The G-Food catering company finds that competitors cater lunch for a group of 100 people for $5 each. The manager of G-Food calculates that for each 25 cent discount per lunch, it is possible to sell an additional 10 lunches. If each lunch costs G-Food$2 to prepare, how many lunches should be prepared to maximize the profit?

The problem gives you a "base" of $5 each for 100 people- for the purposes of this problem I would interpret that as "if you charge$5 for each lunch, you will sell 100 lunches". Now, "for each 25 cent discount per lunch, it is possible to sell an additional 10 lunches.". Okay, let n, be the "number of '25 cent discounts'". Then the charge for each lunch is P= 5- 0.25n ($5 minus 25 cents for each discount). The number of lunches sold will be 100+ 10n (100 plus 10 for each discount). If each lunch costs$2 to prepare, the profit on each lunch is (5- 0.25n)- 2= 3- 0.25n.

The TOTAL profit is, of course, the profit on each lunch times the number of lunches: (3- 0.25n)(100+ 10n). What should n be to make that a maximum? There are several ways to answer that- since that is a quadratic function, completing the square is probably easiest.

And don't forget to ANSWER the question. After you know what n is, calculate the number of lunches that will be sold.

well ye i know how to do that...but we did that last year...this question is from my calculus class...so i don't think its that easy!

Well, if this a calculus class, then it should be even easier- instead of completing the square, take the derivative and set it equal to 0!

wat do u mean?

## 1. What is the revenue problem for G-Food Catering?

The revenue problem for G-Food Catering is that they are not earning enough profit from their catering services. Despite having a steady flow of customers, their profits are not maximizing.

## 2. How can maximizing profit help G-Food Catering?

Maximizing profit can help G-Food Catering by increasing their overall revenue and allowing them to invest in their business, expand their services, and improve their overall financial stability.

## 3. What factors contribute to the revenue problem for G-Food Catering?

There are several factors that may contribute to the revenue problem for G-Food Catering, such as inefficient pricing strategies, high operating costs, lack of marketing efforts, and ineffective management of resources.

## 4. What strategies can be used to solve the revenue problem for G-Food Catering?

Some strategies that can be used to solve the revenue problem for G-Food Catering include conducting market research to understand customer demand and preferences, optimizing pricing strategies, reducing operating costs, and implementing effective marketing campaigns.

## 5. How can a scientist help G-Food Catering solve their revenue problem?

A scientist can help G-Food Catering by analyzing data and conducting experiments to identify the root cause of the revenue problem. They can also provide data-driven solutions and recommendations to help G-Food Catering maximize their profit and solve their revenue problem.

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