Question

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

they ask for three functions, so let's approach them one at a time
for cost, we need to add the overhead and production costs:
C(x) = (over head cost) + (production cost per mower)(number of mowers)

revenue is total income before subtracting costs. in other words, it's just selling price per mower * number of mowers

R(x) = (selling price per mower)(number of mowers)

and profit is simply revenue minus costs

now that the skeletons have been set up for each equation, should be easy to fill in the details