Answer:
The cost function is [tex]C(x)=100000+x\cdot 28[/tex]
The revenue function is [tex]R(x)=x\cdot 74[/tex]
The profit function is [tex]P(x)=46x-100000[/tex]
Step-by-step explanation:
We have the following definitions:
The cost function consists of variable costs and fixed costs and is given by
[tex]C(x)=fixed\:costs+x\cdot variable\:costs[/tex]
The revenue function is given by
[tex]R(x)=x\cdot p(x)[/tex]
where x are the units sold and p(x) is the price per unit.
The profit function is given by
[tex]P(x)=R(x)-C(x)[/tex]
Given:
Fixed costs = $100,000
Variable costs = $28 per unit
Price per unit = $74 per unit
Applying the above definitions and the information given, we get that:
The cost function is [tex]C(x)=100000+x\cdot 28[/tex]
The revenue function is [tex]R(x)=x\cdot 74[/tex]
The profit function is [tex]P(x)=74x-(28x+100000)=46x-100000[/tex]
