A tire company determines that to manufacture a certain type of tire, it costs $9000 to set up the production process. Each tire that is produced costs $21 in material and labor. The company sells this tire to wholesale distributors for $49 each.

(a) Find a linear function C that models the total cost

C(x)
of producing x tires.

C(x) =

I got 9000+21x

(b) Find a linear function R that models the revenue

Not sure

R(x)
from selling x tires.

R(x) =

Also not sure

(c) Find a linear function P that models the profit P(x) from selling x tires. [Note: profit = revenue − cost.]

C = 9000 + 21 x yes

Revenue = R = 49 x

P = 49 x - 21 x - 9000
so
P = 28 x - 9000

now for some reason they did not asdk how ma tires must be sold to break even but it would be
P = 0
28 x = 9000
x = 9000/28

revenue=49x

profit=revenue-cost

To find the linear function C(x) that models the total cost of producing x tires, we know that the fixed cost (the cost to set up the production process) is $9000, and the variable cost (the cost per tire in material and labor) is $21.

The linear function C(x) can be represented as:
C(x) = fixed cost + (variable cost per tire * number of tires produced)

Substituting the given values:
C(x) = 9000 + (21x)

Therefore, the linear function C(x) that models the total cost of producing x tires is C(x) = 9000 + 21x.

For the linear function R(x) that models the revenue from selling x tires, we know that the selling price per tire is $49.

The linear function R(x) can be represented as:
R(x) = price per tire * number of tires sold

Substituting the given values:
R(x) = 49x

Therefore, the linear function R(x) that models the revenue from selling x tires is R(x) = 49x.

To find the linear function P(x) that models the profit P(x) from selling x tires, we subtract the total cost (C(x)) from the revenue (R(x)).

P(x) = R(x) - C(x)

Substituting the given values for C(x) and R(x):
P(x) = 49x - (9000 + 21x)

Simplifying the equation:
P(x) = 49x - 9000 - 21x

Combining like terms:
P(x) = 28x - 9000

Therefore, the linear function P(x) that models the profit P(x) from selling x tires is P(x) = 28x - 9000.

(a) To find the linear function C(x) that models the total cost of producing x tires, we need to consider the fixed cost and the variable cost per tire.

The fixed cost to set up the production process is $9000, which remains constant regardless of the number of tires produced.

The variable cost per tire is the cost of materials and labor, which is given as $21.

Therefore, the linear function C(x) for the total cost can be modeled as:
C(x) = Fixed cost + Variable cost per tire * Number of tires
C(x) = $9000 + $21x

(b) To find the linear function R(x) that models the revenue from selling x tires, we need to consider the selling price per tire.

The selling price per tire to wholesale distributors is $49.

Therefore, the linear function R(x) for the revenue can be modeled as:
R(x) = Selling price per tire * Number of tires
R(x) = $49x

(c) To find the linear function P(x) that models the profit P(x) from selling x tires, we need to subtract the cost function C(x) from the revenue function R(x).

Profit = Revenue - Cost

P(x) = R(x) - C(x)
P(x) = ($49x) - ($9000 + $21x)
P(x) = $49x - $9000 - $21x
P(x) = $28x - $9000