Mathematics 2019 JAMB Past Questions - Question 37: A trader realizes 10x –x2 naira profit from the sale of x bags of corn. How many bags will give him the maximum profit?

Correct Answer

B

Explanation

To find the number of bags that will give the trader the maximum profit, we can use the formula for the vertex of a parabola, which represents the profit function in this case. The profit function is given by \( P(x) = 10x - x^2 \).The x-coordinate of the vertex of the parabola representing the profit function can be found using the formula \( x = -\frac{b}{2a} \), where the profit function is in the form \( ax^2 + bx + c \).In this case, the profit function is \( P(x) = -x^2 + 10x \), so we can identify \( a = -1 \) and \( b = 10 \). Substituting these values into the formula gives:\[ x = -\frac{10}{2(-1)} = -\frac{10}{-2} = 5 \]So, the trader will realize the maximum profit when he sells 5 bags of corn. Therefore, the correct answer is B. 5 bags.