Solve the problem.
-The revenue achieved by selling x graphing calculators is figured to be x(50 - 0.5x) dollars. The cost of each calculator is $14. How many graphing calculators must be sold to make a profit (revenue - cost) of at least
$630.00?
A) $\{ x \mid 32

Question

Solve the problem.
-The revenue achieved by selling x graphing calculators is figured to be x(50 - 0.5x) dollars. The cost of each calculator is $14. How many graphing calculators must be sold to make a profit (revenue - cost) of at least
$630.00?
A) $\{ x \mid 32 < x < 40 \}$
B) $\{ x \mid 30 < x < 42 \}$
C) $\{ x \mid 39 < x < 51 \}$
D) $\{ x \mid 31 < x < 41 \}$

Quizplus · Accepted Answer

First, we calculate the profit function by subtracting the total cost from the revenue. The revenue function is $R(x) = x(50 - 0.5x)$ and the cost function is $C(x) = 14x$. Thus, the profit function $P(x) = R(x) - C(x) = x(50 - 0.5x) - 14x = x(36 - 0.5x)$. To find the number of calculators $x$ that results in a profit of at least $630, we set $P(x) \geq 630$: $x(36 - 0.5x) \geq 630$. Simplifying gives $36x - 0.5x^2 \geq 630$, or $0.5x^2 - 36x + 630 \leq 0$. Factoring or using the quadratic formula gives the range of $x$ that satisfies this inequality. Solving the quadratic inequality, we find the values of $x$ that make the inequality true, which corresponds to the interval $30 < x < 42$, matching choice B.

Solve the Problem {x∣32<x<40}\{ x \mid 32 < x < 40 \}{x∣32<x<40}

Solve the Problem $\{ x \mid 32 < x < 40 \}$