Question

A company has fixed monthly costs of $130,000 and production costs on its product of $32 per unit. The company sells its product for $66 per unit. The cost function, revenue function and profit function for this situation are a)C(x) = 32x+ 130000 ; R(x) = 66x; P(x) = 34x+ 130000b)C(x) = 66x+ 10858 ; R(x) = x+ 13 ; P(x) = − 34x+ 130000c)C(x) = 32x+ 130000 ; R(x) = 66x; P(x) = 34x− 130000d)C(x) = 66x; R(x) = 32x+ 130000 ; P(x) = − 34x+ 130000e)C(x) = 32x− 130000 ; R(x) = 66x; P(x) = 34x− 130000

Answer 1

Answer:

The cost function is $C(x)=32x+130000$.

The revenue function is $R(x)=66x$.

The profit function is $P(x)=34x-130000$.

Step-by-step explanation:

We have the following definitions:

The cost function is a mathematical formula that gives the total cost to produce a certain number of units. It consists of variable costs and fixed costs and is given by

$C(x)=(fixed \:cost)+x\cdot (variable \:cost)$

If $x$ units are sold and the price per unit is $p(x)$, then the total revenue is

$R(x)=x\cdot p(x)$

and $R(x)$ is called the revenue function.

If $x$ units are sold, then the total profit is

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

and $P(x)$ is called the profit function.

Applying the above definitions we get that:

We know that the company has fixed monthly costs of $130,000 and production costs on its product of $32 per unit.

Therefore,

The cost function is $C(x)=32x+130000$.

We know that the company sells its product for $66 per unit.

Therefore,

The revenue function is $R(x)=66x$.

The profit function is

$P(x)=R(x)-C(x)\\P(x)=66x-(32x+130000)\\P(x)=34x-130000$