Solve the rational inequality. Write the solution set in interval notation.
-The profit made when t units are sold, t 0, is given by $P = t ^ { 2 } - 30 t + 200$ Determine the number of units to be sold in order for P = 0 (the break- even point).
A) t = -10 or t = -20
B) t = 30
C) t 10
D) t = 10 or t = 20

Question

Solve the rational inequality. Write the solution set in interval notation.
-The profit made when t units are sold, t > 0, is given by $P = t ^ { 2 } - 30 t + 200$ Determine the number of units to be sold in order for P = 0 (the break- even point).
A) t = -10 or t = -20
B) t = 30
C) t > 10
D) t = 10 or t = 20

Quizplus · Accepted Answer

To find the break-even point, we set $P = 0$ and solve the quadratic equation $t^2 - 30t + 200 = 0$. Factoring the equation gives $(t - 10)(t - 20) = 0$, which has solutions $t = 10$ and $t = 20$. These are the points where the profit is zero, indicating the break-even points.

Solve the Rational Inequality P=t2−30t+200P = t ^ { 2 } - 30 t + 200P=t2−30t+200

Solve the Rational Inequality $P = t ^ { 2 } - 30 t + 200$