Question

The production cost for a t-shirt printing company is a function of the number of t-shirts that are printed, t. The function that models the production cost is f(t) = 0.1t2 − 6t + 100. How many t-shirts does the company have to print for its production cost to be $40 or less? Enter your answers whole numbers.

Answer 1

Answer:

Therefore the company have to print either 47 or 12 t-shirt for its production cost to be $40 or less.

Step-by-step explanation:

Given that,

The function that models the production cost is

$f(t)=0.1 t^2-6t+100$

To find the number of t-shirt, we put f(t)=40 in given function.

∴40= 0.1t²-6t+100

⇒ 0.1t²-6t+100-40=0

⇒0.1 t²- 6t +60=0

⇒t²-60t+600=0

Applying quadratic formula $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$, a=1, b= - 60 and c=600

$t=\frac{-(-60)\pm\sqrt{(-60)^2-4.1.600}}{2.1}$

  = 47.32,12.67

 ≈47, 12

Therefore the company have to print either 47 or 12 t-shirt for its production cost to be $40 or less.