Question

Manufacturing companies usually have two types of costs. Fixed costs: sometimes called overhead: are costs that are not related to the number of items manufactured. Fixed costs include things like rent: a base level of utilities: and a base level of salaries and must be paid even if the company does not make any products. Variable costs depend on the number of items manufactured. Variable costs include things like parts and raw materials for the products: higher utilities: and higher salaries. As a manufacturing company increases the number of items it produces, the fixed costs do not change, but the variable costs increase.

One company manufactures high-end racing bicycles. The monthly fixed costs are $2140. The total cost to manufacture 21 bikes is $13480. Assume that total cost, C, is linearly related to the number of bicycles, x, that the company manufactures.

A) The cost function is:

Answer 1

The cost function for the company that manufactures high-end racing bicycles can be represented as C(x) = F + Vx, where F is the fixed costs of $2140, and V is the variable cost per bicycle, which is calculated using the provided total cost for 21 bicycles.

Step-by-step explanation:

The student asked about calculating the cost function for a company that manufactures high-end racing bicycles, knowing that fixed costs are $2140 and the total cost for 21 bikes is $13480. Since the cost function C is linearly related to the number of bicycles x, we can express it as C(x) = F + Vx, where F represents the fixed costs and V is the variable cost per bicycle.

Given that the fixed costs (F) are $2140 and the cost of producing 21 bicycles is $13480, we have the following equation for 21 bicycles: C(21) = $2140 + 21V = $13480. Solving for V gives us the variable cost per bicycle. Once we determine V, we will plug it back into the cost function equation to get the complete cost function for the company.