Question

Select the correct functions.

The cost of manufacturing lawn mowers is $12,320 in overhead costs and $396 per lawn mower in production costs. Marketing studies show that the best selling price is $452 per lawn mower. Find the cost function, C(x), the revenue function, R(x), and the profit function, P(x), that model this scenario for x lawn mowers manufactured and sold.

Answer 1

The cost function is C(x) = $12,320 + $396x, the revenue function is R(x) = $452x, and the profit function is P(x) = $56x - $12,320.

Cost Function (C(x)): The cost function is $12,320 plus $396 per lawn mower, multiplied by the number of lawn mowers (x). C(x) = 12,320 + 396x

Revenue Function (R(x)): The revenue function is $452 per lawn mower, multiplied by the number of lawn mowers (x). R(x) = 452x

Profit Function (P(x)): The profit function is the revenue minus the cost.

P(x) = 452x - (12,320 + 396x)

Simplifying,

P(x) = 56x - 12,320

Hence, the cost function is C(x) = $12,320 + $396x, the revenue function is R(x) = $452x, and the profit function is P(x) = $56x - $12,320.