Question

Cost, Revenue, and Profit A company invests $98,000 for equipment to produce a new product. Each unit of the product costs $12.20 and is sold for $16.98. Let x be the number of units produced and sold. (a) Write the total cost C as a function of x. C(x) = 98000+16.98x (b) Write the revenue R as a function of x. R(x) = 207.156 (c) Write the profit P as a function of x. P(x) = 4.78

Answer 1

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

$C(x)=98000+12.20x$

Therefore, the cost function is $C(x)=98000+12.20x$.

Selling price of each unit = Revenue from each unit =  $16.98.

Total revenue = Revenue from x units

$R(x)=16.98x$

Therefore, the revenue function is $R(x)=16.98x$.

Profit = Revenue - Cost

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

$P(x)=16.98x-(98000+12.20x)$

$P(x)=16.98x-98000-12.20x$

$P(x)=4.78x-98000$

Therefore, the profit function is $P(x)=4.78x-98000$.