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The Mad Hatter is ordering cups from Teacups

Limited, for his tea party. The Tescups, Limited catalog

prices cups according to the number of cups ardered. For

orders of 20 or fewer cups, the price is $1.40 per cup plus

$12 shipping and handling on the order. For orders of

more than 20 cups, the price is $1.10 per cup plus $15

shipping and handling

a) Create a piece wise function to describe the

price of cups

b) How much will it cost the Mad Hatter if he orders

20 cups?

Respuesta :

a) The piecewise function is:

[tex]C(n) = 12 + 1.40n, n \leq 20[/tex]

[tex]C(n) = 15 + 1.1n, n > 20[/tex]

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:

[tex]C(n) = 12 + 1.40n, n \leq 20[/tex]

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

[tex]C(n) = 15 + 1.1n, n > 20[/tex]

Then, the piece-wise function is:

[tex]C(n) = 12 + 1.40n, n \leq 20[/tex]

[tex]C(n) = 15 + 1.1n, n > 20[/tex]

Item b:

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

Then:

[tex]C(20) = 12 + 1.4(20) = 12 + 28 = 40[/tex]

It will cost $40.

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

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