Shipping company IPS has shipping rates that are a function of the weight of the parcel. For packages weighing less than or equal to 4 pounds, they charge $1 per pound. For packages weighing between 4 and 14 pounds, they charge $1.75 per pound. If packages weigh 14 pounds or more, they charge $2.75 per pound. IPS refuses to ship any parcel weighing more than 61 pounds. There is also a flat fee of $1.5 for all deliveries and an additional fee of $3 for all deliveries weighing 14 pounds or more.
Complete the following description of a piecewise function so that is describes the shipping costs C(x) ______ in dollars as a function of the weight x in pounds.
C(x) = {_____} if 0 C(x) = {_____} if 4 C(x) = {_____} if 14≤x≤61
How does it cost to ship a package weighing 28 pounds with IPS? $
C(x) = {
1x if 0 < x ≤ 4,
1.75x if 4 < x ≤ 14,
2.75x if 14 < x ≤ 61,
}
To ship a package weighing 28 pounds with IPS:
C(28) = 1.75(28) = $49.
C(x) =
- 1x if 0 < x ≤ 4
- 1.75x if 4 < x ≤ 14
- 2.75x if 14 ≤ x ≤ 61
To calculate the cost of shipping a package weighing 28 pounds with IPS, we need to determine which part of the piecewise function applies.
Since 14 < 28 ≤ 61, the function C(x) = 2.75x applies.
C(28) = 2.75 * 28 = $77
Therefore, it would cost $77 to ship a package weighing 28 pounds with IPS.