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

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

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=(-b\pm√(b^2-4ac))/(2a)`, a=1, b= - 60 and c=600

`t=(-(-60)\pm√((-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.