# Find the maximum profit that a company can make, if the profit function is given by P (x) = 72 + 42 - x^2 , where x is the number of units and P is the profit in rupees.

Find the maximum profit that a company can make, if the profit function is given by P (x) = 72 + 42 - x2. Check out below to know the answer.

by Maivizhi A

**Updated **Mar 07, 2024

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## Find the maximum profit that a company can make, if the profit function is given by P (x) = 72 + 42 - x^2 , where x is the number of units and P is the profit in rupees.

The maximum profit the company can make is ₹513.

Here's how:

Given : P (x) = 72 + 42 - x^2

Quadratic equation : ax^2 + bx + c

When we substitute the given equation,

a = -1

b = 42

c = 72

The x-coordinate of the vertex is given by the formula: x = -b / (2a).

Now,

x = - 42 / (2 x (-1))

x = 21

We need to substitute x = 21 into the function:

P(21) = 72 + 42 * 21 - 21²

P(21) = 513

Therefore, the maximum profit the company can make is ₹513.

## Examples Sums to Work out

- A bakery sells cupcakes at a price of $3 per cupcake. The cost function to produce x cupcakes is given by C(x) = 2x + 10, where x is the number of cupcakes produced and C(x) is the cost in dollars. Determine the maximum profit the bakery can make.
- A toy manufacturer sells remote-controlled cars at a price of $25 each. The cost function to produce x cars is given by C(x) = 5x + 100, where x is the number of cars produced and C(x) is the cost in dollars. Calculate the maximum profit the toy manufacturer can achieve.
- A farmer sells pumpkins at a price of $8 each. The cost function to grow x pumpkins is given by C(x) = 0.5x^2 + 20, where x is the number of pumpkins grown and C(x) is the cost in dollars. Find the maximum profit the farmer can earn.

## Find the maximum profit that a company can make, if the profit function is given by P (x) = 72 + 42 - x2 , where x is the number of units and P is the profit in rupees - FAQs

### 1. What is the maximum profit earned by the company?

The maximum profit the company can make is ₹513.

### 2. What is the given equation?

72 + 42 - x^2

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