Question

A manufacturer has a monthly fixed cost of $110,000 and a production cost of $14 for each unit produced. The product sells for $20 per 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 or loss corresponding to a production level of 12,000 and 23,000 units. (Input a negative value to indicate a loss.)

at 12,000 units $ ______

at 23,000 units $______

Answer 1

Cost function C(x) == FC + VC*Q

Revenue function R(x) = Px * Q

Profit function P(x) =(Px * Q)-(FC + VC*Q)

P(12000) = -38000 Loss

P(23000) = 28000 profit

Explanation:

Total Cost is Fixed cost plus Variable cost multiplied by the produce quantity.

(a)Cost function

C(x) = FC + vc*Q

Where

FC=Fixed cost

VC=Variable cost

Q=produce quantity

(b)

Revenue function

R(x) = Px * Q

Where

Px= Sales Price

Q=produce quantity

(c) Profit function

Profit = Revenue- Total cost

P(x) =(Px * Q)-(FC + vc*Q)

(d) We have to replace in the profit function

at 12,000 units

P(12000) =($20 * 12,000)-($110,000 + $14*12,000)

P(12000) = -38000

at 23,000 units

P(x) =($20 * 23,000)-($110,000 + $14*23,000)

P(23000) = 28000