Question

Manufacturing companies usually have two types of costs.
(a) 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.
(b) 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:
(B) The total cost to manufacture 47 bikes is $______
(C) The cost to produce each additional bike is $_____.

Answer 1

Answer:

(A) 2,140 + 540x

(B) $27,520

(C) $540

Explanation:

Given that,

Fixed cost = $2,140 per month

Total cost to manufacture 21 bikes = $13,480

Variable cost for manufacturing 21 bikes:

= Total cost - Fixed cost

= $13,480 - $2,140

= $11,340

Variable cost for each bike:

= Total variable cost ÷ No. of bikes manufacture

= $11,340 ÷ 21

= $540 per bike

Let the number of bikes manufacture be x

(A) The cost function is as follows:

= Fixed cost + Variable cost

= 2,140 + 540x

(B) The total cost to manufacture 47 bikes:

= Fixed cost + Variable cost

= $2,140 + ($540 × 47)

= $2,140 + $25,380

= $27,520

(C) The cost to produce each additional bike:

= Variable cost for each bike

= $540