Solve the problem.
-The cost of producing $\mathrm { t }$ units is $\mathrm { C } = 4 \mathrm { t } ^ { 2 } + 8 \mathrm { t }$, and the revenue generated from sales is $\mathrm { R } = 5 \mathrm { t } ^ { 2 } + \mathrm { t }$. Determine the number of units to be sold in order to generate a profit.
A) $t 9$
B) $t 0$
C) $t 7$
D) $t 8$

Question

Solve the problem.
-The cost of producing $\mathrm { t }$ units is $\mathrm { C } = 4 \mathrm { t } ^ { 2 } + 8 \mathrm { t }$, and the revenue generated from sales is $\mathrm { R } = 5 \mathrm { t } ^ { 2 } + \mathrm { t }$. Determine the number of units to be sold in order to generate a profit.
A) $t > 9$
B) $t > 0$
C) $t > 7$
D) $t > 8$

Quizplus · Accepted Answer

Profit occurs when revenue exceeds cost, so we set $R > C$ and solve for $t$: $5t^2 + t > 4t^2 + 8t$, simplifying to $t^2 - 7t > 0$, which factors to $t(t - 7) > 0$. This inequality is true for $t > 7$, indicating that more than 7 units must be sold for a profit.

Solve the Problem t\mathrm { t }t Units Is C=4t2+8t\mathrm { C } = 4 \mathrm { t } ^ { 2 } + 8 \mathrm { t }C=4t2+8t

Solve the Problem $\mathrm { t }$ Units Is $\mathrm { C } = 4 \mathrm { t } ^ { 2 } + 8 \mathrm { t }$