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
[tex]Marginal \ profit = \dfrac{dP}{dx} = \dfrac{dR}{dx} - \dfrac{dC}{dx}[/tex]
Where;
P = Profit, R = Revenue, and C = Cost
Therefore, we have;
[tex]Marginal \ profit = \dfrac{d}{dx} \left (4 \cdot x^2 - 5 \cdot x + 10\right) = 8 \cdot x - 5[/tex]
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
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