Question

Suppose that the total profit in hundreds of dollars from selling x items is given by P(x) =4x2 - 5x + 10. Find the marginal profit at x=5

Answer 1

The marginal profit is the profit that an individual or firm earns from producing and selling an additional item

The marginal profit at x = 5 is $3,500

The reason the above value is correct is as follows:

The given total profit function is P(x) = 4·x² - 5·x + 10

Where;

P(x) = The total profit in hundreds of dollars

x = The number items sold

The marginal profit is given by the derivative of the profit function

$Marginal \ profit = \dfrac{dP}{dx} = \dfrac{dR}{dx} - \dfrac{dC}{dx}$

Where;

P = Profit, R = Revenue, and C = Cost

Therefore, we have;

$Marginal \ profit = \dfrac{d}{dx} \left (4 \cdot x^2 - 5 \cdot x + 10\right) = 8 \cdot x - 5$

Marginal profit in hundreds of dollars = 8·x - 5

Therefore, the marginal profit at x = 5, is given as follows;

Marginal profit = 8 × 5 - 5 = 35

The marginal profit at x = 5 is $3,500

Learn more about marginal profit here:

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