To find the profit when 150 televisions are sold, we need to calculate both the revenue and the cost for producing and selling these televisions, and then determine their difference.
### Step-by-Step Solution:
1. Identify the Revenue Function:
The revenue function is given by:
[tex]\[
R(x) = 3x^2 + 180x
\][/tex]
2. Identify the Cost Function:
The cost function is given by:
[tex]\[
C(x) = 3x^2 - 160x + 300
\][/tex]
3. Calculate Revenue for 150 Televisions:
Substitute [tex]\( x = 150 \)[/tex] into the revenue function:
[tex]\[
R(150) = 3(150)^2 + 180(150)
\][/tex]
Evaluating the expression:
[tex]\[
R(150) = 3(22500) + 27000 = 67500 + 27000 = 94500
\][/tex]
So, the revenue for selling 150 televisions is \[tex]$94,500.
4. Calculate Cost for 150 Televisions:
Substitute \( x = 150 \) into the cost function:
\[
C(150) = 3(150)^2 - 160(150) + 300
\]
Evaluating the expression:
\[
C(150) = 3(22500) - 24000 + 300 = 67500 - 24000 + 300 = 43800
\]
So, the cost for producing 150 televisions is \$[/tex]43,800.
5. Calculate Profit:
Profit is the difference between revenue and cost:
[tex]\[
\text{Profit} = R(150) - C(150) = 94500 - 43800 = 50700
\][/tex]
Therefore, the profit for selling 150 televisions is \[tex]$50,700.
### Conclusion:
The correct answer is:
\[
\boxed{\$[/tex]50,700}
\]
