QuestionFor the function $P(x)=-0.74 x^{2}+22 x+75$, what constraints ensure profits are at least \$175,000? Options:$-3.09 \leq x \leq 5.6$or$0 \leq x < 5.6$?

Studdy Solution
The solutions to the inequality $-0.74 x^{}+22 x -100 \geq0$ are the intervals $(-\infty, x_{}] \cup [x_{}, \infty)$, where $x_{}$ and $x_{}$ are the roots of the quadratic equation. However, since $x$ represents the number of calculators produced, it cannot be negative. Therefore, the reasonable constraints for the model are $0 \leq x \leq5.6$ and $24.13 \leq x$.
The correct answer is $0 \leq x \leq5.6$ and $24.13 \leq x$.