Given:
Investment on equipment = $98,000
Cost of each unit = $12.20
Selling price of each unit = $16.98.
To find:
(a) The total cost C as a function of x.
(b) The revenue R as a function of x.
(c) The profit P as a function of x.
Solution:
Let x be the number of units produced and sold.
We have,
Fixed cost = $98,000
Variable cost = $12.20x
Total cost = Fixed cost + Variable cost
[tex]C(x)=98000+12.20x[/tex]
Therefore, the cost function is [tex]C(x)=98000+12.20x[/tex].
Selling price of each unit = Revenue from each unit = $16.98.
Total revenue = Revenue from x units
[tex]R(x)=16.98x[/tex]
Therefore, the revenue function is [tex]R(x)=16.98x[/tex].
Profit = Revenue - Cost
[tex]P(x)=R(x)-C(x)[/tex]
[tex]P(x)=16.98x-(98000+12.20x)[/tex]
[tex]P(x)=16.98x-98000-12.20x[/tex]
[tex]P(x)=4.78x-98000[/tex]
Therefore, the profit function is [tex]P(x)=4.78x-98000[/tex].
