8 A company expects fixed costs of 25000 and variable costs

8. A company expects fixed costs of $25,000 and variable costs of $95 per item. Each item retails for $200.

a. State the cost, revenue, and profit functions.

b. If 100 units are produced, state the total cost, revenue generated, and the profit earned.

c. Find the number of items the company must produce to break even. Also find the revenue they must generate to break even.

Solution

Let the number of items manufactured be x

a) Cost Function C(x) = Variable Costs + Fixed Costs = 95x + 25000

Revenue = Selling Price * number of units = 200x

Profit Function = Revenue - CostFunction = 200x - (95x + 25000) = 105x - 25000

b) If 100 units are produced

Total Cost = 95(100) + 25000 = 34500$

Revenue Generated = 200(100) = 20000$

Profit earned = 20000 - 34500 = -14500$

c) For the break even point

Profit = 0

105x - 25000 = 0

x = 25000/105 = 238.09 units

Revenue they must generate to break even = 200(239) = 47800$