Video games sold: [tex] x [/tex]

Revenue function: [tex] R(x) = 60x [/tex]

Cost function: [tex] C(x) = 12 + 7x [/tex]

Profit function: [tex] P(x) = \square [/tex]

What is the profit earned from selling 20 video games? [tex] \square [/tex]



Answer :

To find the profit earned from selling 20 video games, let's go through the problem step-by-step.

1. Determine the Revenue Function [tex]\( R(x) \)[/tex]:

The revenue function is given by [tex]\( R(x) = 60x \)[/tex]. Here, `x` represents the number of video games sold.

Since we need to find the revenue from selling 20 video games, substitute [tex]\( x = 20 \)[/tex] into the revenue function:
[tex]\[ R(20) = 60 \times 20 = 1200 \][/tex]

2. Determine the Cost Function [tex]\( C(x) \)[/tex]:

The cost function is given by [tex]\( C(x) = 12 + 7x \)[/tex].

Substitute [tex]\( x = 20 \)[/tex] into the cost function to find the total cost for 20 video games:
[tex]\[ C(20) = 12 + 7 \times 20 = 12 + 140 = 152 \][/tex]

3. Determine the Profit Function [tex]\( P(x) \)[/tex]:

The profit function is defined as the revenue minus the cost, [tex]\( P(x) = R(x) - C(x) \)[/tex].

Substitute [tex]\( R(20) \)[/tex] and [tex]\( C(20) \)[/tex] into the profit function to find the profit:
[tex]\[ P(20) = R(20) - C(20) = 1200 - 152 = 1048 \][/tex]

Therefore, the profit earned from selling 20 video games is [tex]\( 1048 \)[/tex].