Justin started a lawn maintenance business. His basic rate to maintain an averag

Question

Justin started a lawn maintenance business. His basic rate to maintain an average size lawn is $35. It cost Justin $550 to start the business (trailer, equipment, etc.) and he estimates that his cost per lawn is $1.50 (gas, oil, blades, etc.). Show work for all calculations and give concise explanations when necessary. a) Write the cost function in terms of the revenue function in terms of r(x), and the profit function in terms p(x) in simplest form of for Justin's business. b) Set up an equation use algebra to find the number of lawns that Justin has to maintain for his business to break even (cost equal to revenue). c) Find and interpret the meaning of p(250). d) Set up an equation and use algebra to find when Justin's business will make a profit of $25.000? e) Sketch the cost and revenue functions on the same graph.

Explanation / Answer

a) Let 'x' be number of lawns

C(x) = 550 + 1.5x

r(x) = 35x

P(x) = r(x) - C(x) = 35x - 550 - 1.5x = 33.5x - 550

b) At breakeven:

r(x) = C(x)

35x = 550 + 1.5x

x = 16.42 or 17 lawns

c) P(250) is when there are 250 lawns then profit is:

P(x) = 33.5x - 550

P(250) = 33.5*250 - 550 = 7825$

d) 25000 = 33.5x - 550

x = 763 lawns

Related Questions

Navigate

• Browse (All)
• Browse J
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.