Justin started a lawn service business. His rate to maintain an average size lawn is $35. It costs Justin $750 to start the business. And he estimates that his cost per lawn is $1.50. Write the cost function in terms of c (x) the revenue terms of r (x) and the profit function in terms p (x)

Question

Mathematics

Emelia Wiley

10 December, 12:14

Justin started a lawn service business. His rate to maintain an average size lawn is $35. It costs Justin $750 to start the business. And he estimates that his cost per lawn is $1.50. Write the cost function in terms of c (x) the revenue terms of r (x) and the profit function in terms p (x)

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Ariel Huerta · Answer 1

Step-by-step explanation:

Cost function: Fixed costs + Variable costs

In this case Justin will have to pay $750 to star the business, this is his fixed cost. And then, he will have to pay $1,50 per each lawn, this is his variable cost because it depends on the number of lawns he sells.

C (x) = $750+$1,50x

Revenue function (R (x)):

R (x) = Price * Number of units sold (x)

R (x) = $35*x

Profit function ((P (x)) = Revenue function (R (x)) - Cost function (C (x))

P (x) = $35x - [$750+$1,50x]

P (x) = $33,5-$750