Question

A manufacturer has a monthly fixed cost of $22,500 and a production cost of $6 for each unit produced. The product sells for $9/unit.

a) What is the cost function?
C(X) =

b) What is the revenue function?
R(x) =

c) What is the profit function?
P(X) =

d) Compute the profit (loss) corresponding to production levels of 6,000 and 9,000 units.
P(6,000) =
P(9,000) =

Answer 1

Explanation:

Profit is expressed as Revenue - Cost. Therefore

P = R - C

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

Let x represent the number of units produced and sold.

a) A manufacturer has a monthly fixed cost of $22,500 and a production cost of $6 for each unit produced. This means that the cost function would be

C(x) = 22500 + 6x

b) The product sells for $9/unit. This means that the revenue function would be

R(x) = 9x

c) The profit function would be

P(x) = R(x) - C(x) = 9x - (22500 + 6x)

P(x) = 9x - 22500 - 6x

P(x) = 3x - 22500

d) when x = 6000,

P = 3 × 6000 - 22500 = 18000 - 22500 = -$4500. loss is made

when x = 9000,

P = 3 × 9000 - 22500 = 27000 - 22500 = $4500. profit is made