Piece wise linear functions

Question

A university department is planning to have a local company print custom shirts for them. The quoted price for creating and printing the shirts is as follows:

○The design and set-up fee is $95. ○For orders of up to 75 shirts, each shirt is priced at $14 each. ○For orders of 76 or more shirts, every shirt is priced at $10.50 each.

A) Find a formula for the function that represents the total cost of ordering n shirts from the company.

B) How much would it cost to order 200 shirts?

C) How many shirts could they get with $1400?

Answer 1

A) let P be the total cost of ordering n shirts from the company,

let n be the number of shirts

$95 is a fixed fee, so it's a constant c. Using the formula y = Mn + c

We have P = 14n + 95 (if n </= 75)

and P = 10.50n + 95 (if n >/= 76)

B) Since 200>76, it falls into the second equation.

The n in the second equation should be substituted for 200 to find P.

P = 10.50(200) + 95 = 2100 + 95 = $2195

So, 200 shirts would cost $2195 (that's too expensive, goshh)

C) If 200 shirts cost $2195(from B), then $1400 would get them a lower number of shirts. This means if your answer is greater than 200 shirts, you are absolutely off track. Same thing as B but this time, $1400 is substituted for P. Then n is found.

Answer 2

A)

$95 + $14n if n < 76

Cost =

$95 + $10.50n if n ≥ 76

B) For n = 200 shirts, which formula from A) would you use? Plug in n= 200 and compute the answer

C) Set Cost = $1400 and solve for n. Again, which formula from A) applies?