Problema Solution
Jeremiah has been saving up his money and now wants to start his own business. He wants to open a bicycle shop. He finds a wholesaler where he can purchase bikes for $100 apiece. He also finds that he can purchase a store downtown for $20,000, and will require another $10,000 to get the store ready for his bicycle shop. Consider there two latter costs as fixed costs. Jeremiah plans to sell each bicycle for $250, before tax. Let the independent variable be x.
What does x represent? x=
Develop a cost equation, C(x)=
Develop a revenue equation, R(x)=
Develop a profit equation, P(x)=
If you were to graph C(x) and R(x), what do we call the point where they intersect?
Answer provided by our tutors
let 'x' represent the number of bikes Jeremiah is able to sell
total costs = fixed costs + costs-per-bike:
C(x) = 20000 + 10000 + 100x = 30000 + 100x
total revenue:
R(x) = 250x
profit = revenue - costs:
P(x) = 250x - (30000 + 100x) = 150x - 30000
the graphs will intersect when revenue equal costs, it can be called a 'break even point', although you should consult your course material for the correct terminology
the number of bikes that must be sold in order to break even is found by solving for when profit equals zero:
0 = 150x - 30000
x = 30000/150 = 200
Jeremiah must sell 200 bikes in order to break even