Question

A coach is ordering custom practice T-shirts and game jerseys for each of the team members. The coach orders T-shirts from a local shop that charges $7.50 for each, plus a $35 initial printer fee. The cost of the T-shirts is modeled by 𝑡⁡(𝑥)=7.5⁢𝑥+35, where x is the number of team members. He orders jerseys online, which cost $18 each with $20 shipping. The cost of the jerseys is modeled by 𝑗⁡(𝑥)=18⁢𝑥+20. Define and graph the function that represents the total cost of the T-shirts and jerseys.



a. Identify and write a new function to represent total cost.
b. Graph the function that represents the total cost of the T-shirts and jerseys.

Answer 1

a. Add the two cost functions:
C(x) = t(x) + j(x) = (7.5x + 35) + (18x + 20) = 25.5x + 55.

So the total-cost function is C(x) = 25.5x + 55 (with x the number of team members, x ≥ 0, typically integer).

b. To graph C(x) = 25.5x + 55:
- y-intercept: (0, 55).
- slope: 25.5 (each additional team member raises cost by $25.50).
- Useful points to plot: (0,55), (1,80.5), (2,106), (4,157), (10,310).
Plot those points and draw the straight line through them. (If you restrict to whole team members, plot only the integer x-values.)