Question

The Mad Hatter is ordering cups from Teacups

Answer 1

a) The piecewise function is:

$C(n) = 12 + 1.40n, n \leq 20$

$C(n) = 15 + 1.1n, n > 20$

b) Applying the piecewise function, it is found that it will cost $40.

A piecewise function is a function that has different definitions based on the input.

Item a:

• 20 or fewer cups, fixed cost of $12 for shipping plus $1.40 per cup. Thus, the first definition of the function for the cost of n cups is:

$C(n) = 12 + 1.40n, n \leq 20$

• For more than 20 cups, price of $1.1 per cup plus a shipping and handling fee of $15. Then:

$C(n) = 15 + 1.1n, n > 20$

Then, the piece-wise function is:

$C(n) = 12 + 1.40n, n \leq 20$

$C(n) = 15 + 1.1n, n > 20$

Item b:

• The cost of 20 cups is C(20).
• It is the first definition, which is valid for $n \leq 20$.

Then:

$C(20) = 12 + 1.4(20) = 12 + 28 = 40$

It will cost $40.

A similar problem is given at brainly.com/question/24815096