# How can calculus help maximize profit for Goodfood catering company?

• m0286
In summary, the problem is asking how many lunches should be prepared by Goodfood catering company in order to maximize profit. The cost of each lunch is $2 and the competitors are selling for$5. For every 25 cent discount per lunch, Goodfood can sell an additional 10 lunches. The equation for profit is P = -2.5x^2 + 5x + 300, where x represents the number of discounted lunches. The derivative of this equation is x = 1, meaning that the maximum profit will be achieved when the number of discounted lunches is 1. This corresponds to a profit of $302.50. However, this is not the optimal number of lunches to prepare. To find the optimal number m0286 I am stuck on a calculus problem.. I have most of the answer but I suddenly got confused, and can't figure it out any further, the question is: The goodfood catering company finds that competitors cater lunch for a group of 100 people for$5 each. The manager of Goodfood calculates the for each 25 cent discount per lunch, its possible to sell an additional 10 lunches. If each lunch costs goodfood $2 to prepare, how many lunches should be prepared to maximize profit. This is what I got so far: let P represent profit, let x represent # of discounted of lunches P=(3-0.25x)(100+10x) =-2.5x^2+5x+300 for the derivative i got x=1. When i substituted that into the above equationi got: =-2.5(1)^2+5(1)+300 =302.5 HERES WHERE I AM LOST! Is this 302.5, the amount of profit they make or is this the number of lunches they should make to make greatest profit.? 302.5 is the amount of profit. The price of the lunch is$2.75, which represents X=1. When I wrote the problem out I used:

($5.00-.25x)(100+10x)-(100+10x)(2.00), which is Revenue minus Expenses = Profit. Note that the profit would have been$300 had we not reduced the price. This happens to be the same value we would get if we dropped the price by $.50: ($2.50)(120) = \$300. And it is downhill from there.

Last edited:
Thanks for that help, but would you be able to help me with how I would find how many lunches should be prepared to reach maximum profit?

It is right in the equation, since x=1, the number is 100+10x = 110.

## 1. What is Calculus?

Calculus is a branch of mathematics that deals with the study of change and motion. It involves the use of mathematical concepts such as derivatives and integrals to solve problems related to rates of change, optimization, and prediction.

## 2. Why is Calculus important?

Calculus is essential in many fields, including physics, engineering, economics, and statistics. It allows us to model and analyze real-world situations and make accurate predictions. It also forms the basis for more advanced mathematical concepts and theories.

## 3. How is Calculus used in everyday life?

Calculus is used in various everyday situations, such as calculating the speed and acceleration of moving objects, determining the optimal route for travel, and predicting the growth of populations and economies. It is also used in fields like medicine, where it helps in understanding biological processes and developing new treatments.

## 4. What are the two main branches of Calculus?

The two main branches of Calculus are differential calculus and integral calculus. Differential calculus deals with rates of change and slopes of curves, while integral calculus deals with accumulation and the area under a curve. Both branches are closely related and are used to solve different types of problems.

## 5. Is Calculus difficult to learn?

Calculus can be challenging to learn, but with practice and patience, it can be mastered. It requires a solid understanding of algebra and basic mathematical concepts. One must also be able to think critically and logically to solve complex problems. With dedication and the right resources, anyone can learn Calculus.

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