The cost to produce n shirts is given as:
[tex]C=0.4 n^{2} -32n+650[/tex]
The cost function is a quadratic function with a positive leading coefficient, so the minimum value will be at the vertex of the function.
The vertex of a quadratic function can be calculated as:
[tex]( \frac{-b}{2a},f( \frac{-b}{2a})) [/tex]
a = coefficient of squared term = 0.4
b = coefficient of n term = -32
Using these values, we get:
[tex]- \frac{b}{2a}= - \frac{-32}{0.8}= 40[/tex]
This means, the cost will be minimized if 40 t shirts are produced.
The minimum cost can be found by calculating C at n=40
So, the minimum cost will be:
C(40) = 0.4(40)² - 32(40) + 650
C(40) = 10
Therefore, the minimum cost to produce a t shirt will be $10
