The cost of producing $t$ units is $C = 3 t ^ { 2 } + 9 t$, and the revenue generated from sales is $R = 4 t ^ { 2 } + t$. Determine the number of units to be sold in order to generate a profit.
A) $t 0$
B) $t 8$
C) $t 10$
D) $t 9$

Question

The cost of producing $t$ units is $C = 3 t ^ { 2 } + 9 t$, and the revenue generated from sales is $R = 4 t ^ { 2 } + t$. Determine the number of units to be sold in order to generate a profit.
A) $t > 0$
B) $t > 8$
C) $t > 10$
D) $t > 9$

Quizplus · Accepted Answer

Profit is generated when revenue $R$ exceeds cost $C$. Setting $R > C$, we have $4t^2 + t > 3t^2 + 9t$. Simplifying gives $t^2 > 8t$, or $t(t - 8) > 0$. Thus, $t > 8$.

The Cost of Producing ttt Units Is C=3t2+9tC = 3 t ^ { 2 } + 9 tC=3t2+9t

The Cost of Producing $t$ Units Is $C = 3 t ^ { 2 } + 9 t$