QuestionFind the reasonable constraint for $P(x) = -0.74x^2 + 22x + 75$ to keep profits $\geq \, 175$ (in thousands).

Studdy Solution
This inequality represents the constraint on the number of calculators the company needs to produce to keep its profits at or above $\$175,000$. The solution to this inequality will give us the range of $x$ values (number of calculators in thousands) that satisfy this condition.
The solution to this inequality is not straightforward because it is a quadratic inequality. It requires finding the roots of the quadratic equation and then determining the intervals of $x$ that satisfy the inequality.However, the problem is asking for a reasonable constraint for the model, not the exact solution. Therefore, we can say that a reasonable constraint for the model, based on the given profit function and the desired profit level, is$$-0.74 x^{2}+22 x-100 \geq0$$This means that the company needs to produce a number of calculators (in thousands) that satisfies this inequality in order to keep its profits at or above $\$175,000$.