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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. 

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.

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. 

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Examples Sums to Work out 

  1. 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.
  2. 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.
  3. 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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