Question

The Junior class is selling tee-shirts to raise money for their prom. Tie-Dye-Tees charges the class a $30 set up fee plus $2.50 for each tee-shirt they have printed. The class officers plan to sell the tee-shirts for $10 and are taking pre-orders so that they don't order any extra shirts. If x is the number of tee-shirts that were ordered/sold,
(a) Write the cost function C(x).
(b) Write the revenue function R(x).
(c) Profit is the difference between your revenue and your cost. Write the profit function P(x).
(d) Determine when P(x)=0. What does this mean?

Answer 1

a) well we know that it COSTS 30 to set up..and 2.50 per shirt they print...so
C(x) = 2.50x + 30

b) we know that they want to sell each shirt for 10 so this will just be
R(x) = 10x

c) We can see that Profit = revenue - cost....so subtract our 2 functions
P(x) = 10x - (2.50x + 30)

d) P(x) = 0 this is when our profit = 0...so we simply plug in 0 for P(x) in our above equation...

P(x) = 10x - (2.50x + 30)
0 = 10x - 2.50x - 30
30 = 10x - 2.50x
30 = 7.50x
x = 4

so they need to sell 4 shirts JUST to break even...and START making a profit..

Does this make sense?

Answer 2

Yes. Thank you very much. :)

Answer 3

Anytime :)