Question

A manufacturer has a monthly fixed cost of $100, 000 and a production cost of
$14 for each unit produced. The product sells for $20/unit
1. What is the cost function?
2. What is the revenue function?
3. What is the profit function?
4. Compute the profit (loss) corresponding to production level of 15, 000 units.

Answer 1

Answer:

(a) 100,000 + 14x

(b) R(x) = 20x

(c) P(x) = 6x - 100,000

(d) Loss = $10,000

Explanation:

Fixed cost = $100,000

production cost = $14 for each unit produced

Selling price of product = $20 per unit

Let x be the number of units produced and sold,

(1) Cost function:

C(x) = Fixed cost + production cost

       = 100,000 + 14x

(2) Revenue function:

R(x) = 20x

(3) profit function:

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

       = 20x - (100,000 + 14x)

       = 6x - 100,000

(4) P(x) = 6x - 100,000

At production level = 15,000

P(15,000) = 6(15,000) - 100,000

                = 90,000 - 100,000

                = -10,000

So, there is a loss of $10,000