A school theater group is selling candy to raise funds in order to put on their next performance. The candy cost the group $0.20 per piece. Plus, there was a $9 shipping and handling fee. The group is going to sell the candy for $0.50 per piece. How many pieces of candy must the group sell in order to break even?
Set up the cost function C(p) where p is the number of pieces of candy.
C(p) = Cost per piece * p + shipping and handling fee
C(p) = 0.2p + 9
Set up the Revenue function R(p) where p is the number of pieces of candy.
R(p) = Sale price * p
R(p) = 0.5p
Break-even means zero profit or loss, so we set the Cost Function equal to the Revenue Function
0.2p + 9 = 0.5p
To solve this equation for p, we type it in our math engine and we get:
p = 30
Set up the cost function C(p) where p is the number of pieces of candy.
C(p) = Cost per piece * p + shipping and handling fee
C(p) = 0.2p + 9
Set up the Revenue function R(p) where p is the number of pieces of candy.
R(p) = Sale price * p
R(p) = 0.5p
Break-even means zero profit or loss, so we set the Cost Function equal to the Revenue Function
0.2p + 9 = 0.5p
To solve this equation for p, we type it in our math engine and we get:
p = 30