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]$2,700
B. \$[/tex]6,000
C. \[tex]$50,700
D. \$[/tex]51,300



Answer :

GinnyAnswer
To find the profit when 150 televisions are sold, we need to determine both the revenue and the cost, and then subtract the cost from the revenue. Let's go through the steps in detail.

Step 1: Calculate the Revenue

The revenue function given is:
[tex]\[ \text{Revenue} = 3x^2 + 180x \][/tex]

We need to find the revenue when [tex]\( x = 150 \)[/tex]:
[tex]\[ \text{Revenue} = 3(150)^2 + 180(150) \][/tex]

Perform the calculations:
[tex]\[ 3(150)^2 = 3 \times 22500 = 67500 \][/tex]
[tex]\[ 180(150) = 27000 \][/tex]

So, the revenue is:
[tex]\[ \text{Revenue} = 67500 + 27000 = 94500 \][/tex]

Step 2: Calculate the Cost

The cost function given is:
[tex]\[ \text{Cost} = 3x^2 - 160x + 300 \][/tex]

We need to find the cost when [tex]\( x = 150 \)[/tex]:
[tex]\[ \text{Cost} = 3(150)^2 - 160(150) + 300 \][/tex]

Perform the calculations:
[tex]\[ 3(150)^2 = 3 \times 22500 = 67500 \][/tex]
[tex]\[ 160(150) = 24000 \][/tex]

So, the cost is:
[tex]\[ \text{Cost} = 67500 - 24000 + 300 = 43800 \][/tex]

Step 3: Calculate the Profit

Profit is the difference between revenue and cost:
[tex]\[ \text{Profit} = \text{Revenue} - \text{Cost} \][/tex]
[tex]\[ \text{Profit} = 94500 - 43800 = 50700 \][/tex]

Therefore, the profit when 150 televisions are sold is:
[tex]\[ \boxed{50700} \][/tex]

This matches the option [tex]$\$[/tex] 50,700$.

Other Questions