> #mathematics , #business > A firm has found experience that it's profit(TZS)in term of number of units x produced is given by p=2000+240x-x².find the maximum profit?
Dec 4, 2023

# A firm has found experience that it's profit(TZS)in term of number of units x produced is given by p=2000+240x-x².find the maximum profit?

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Dec 4, 2023
To find the maximum profit, we need to find the vertex of the quadratic equation p = 2000 + 240x - x².

The vertex of a quadratic equation in the form ax² + bx + c is given by the formula x = -b/2a.

In this case, a = -1, b = 240, and c = 2000.

Using the formula, we can calculate the x-coordinate of the vertex:

x = -b/2a = -240/(2*(-1)) = -240/(-2) = 120.

To find the maximum profit, we substitute this value of x back into the equation:

p = 2000 + 240x - x² = 2000 + 240(120) - (120)² = 2000 + 28800 - 14400 = 26400.

Therefore, the maximum profit is TZS 26,400.
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