Question

Need a quick explanation?

Susie wants to start making and selling bracelets. Her costs are the large sum of money that includes her initial investment and the cost of materials for each bracelet. She has already planned how much she is going to sell her bracelets for. Explain how Susie can set up a system of equations to predict when she will start to make a profit.

Answer 1

@wolf1728

Answer 2

f(x) = px - cx - f(o) where f(x) is the current money, x is the number of bracelets sold, p is the price a bracelet was sold for, c is the cost of making a bracelet, and f(o) is the initial investment.

To find the point where Susie will begin to make a profit, set f(x) to zero and solve for px algebraically.

0 = px - cx - f(o)
cx + f(o) = px

When value of px is greater than the value of cx + f(o) Susie will have made a profit.


Aside: If your teacher wants you to start with 2 equations as opposed to one, let i(x) = px and s(x) =cx + f(o) where i(x) is the income generated and s(x) is the spent money. At the equilibrium point (where Susie will begin to make a profit), the income and the spent money should be equal. This implies that px = cx + f(o) at this point since i(x) = s(x).

Answer 3

Thank you! That was alot to take in xD