Answered

Profit is the difference between revenue and cost. The revenue, in dollars, of a company that manufactures televisions can be modeled by the polynomial [tex]3x^2 + 180x[/tex]. The cost, in dollars, of producing the televisions can be modeled by [tex]3x^2 - 160x + 300[/tex]. The variable [tex]x[/tex] is the number of televisions sold.

If 150 televisions are sold, what is the profit?

A. [tex]$\$[/tex]2,700[tex]$

B. $[/tex]\[tex]$6,000$[/tex]

C. [tex]$\$[/tex]50,700[tex]$

D. $[/tex]\[tex]$51,300$[/tex]



Answer :

GinnyAnswer
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: \[ \boxed{\$[/tex]50,700}
\]