Final answer:
Dalco Manufacturing should produce 1,000 units per week to earn the maximum profit. The maximum weekly profit is calculated to be $1400. The formula for finding the vertex of the profit function was used to determine the quantity of units produced for maximizing profits.option c is correct answer.
Step-by-step explanation:
To find out how many units Dalco Manufacturing should produce per week to earn the maximum profit, we need to analyze the quadratic profit function P = -5x2 + 10x + 9, where P is the profit in hundreds of dollars and x is the number of units in thousands.
To maximize the profit, we need to find the vertex of this parabola, which can be found using the formula -b/(2a) for the x-coordinate. In this case, a=-5 and b=10, so the vertex occurs at x = -10/(2*(-5)) = 1. This means that the company should produce 1,000 units to maximize profits.
To find the maximum weekly profit, we substitute x = 1 into the profit function: P = -5(1)2 + 10(1) + 9 = -5 + 10 + 9 = 14. Since P represents hundreds of dollars, the maximum weekly profit is $1400.
Thus, the correct answer to the question is: c. 1,000 units; $1400.