A courier company charges P300 per package weighing 4kg or less. They charge P30 for each additional kilogram or fraction of a kilogram up to 7 kg. Write a piecewise function that gives the cost C for shipping a package weighing k kilograms.
Answers
Let the cost of 1 kg onion , 1 kg wheat and 1 kg of rice be Rsx,Rsy,Rsz respectively.
So, 4x+3y+2z=60
2x+4y+6z=90
6x+2y+3z=70
These equations can be written as
AX=B
where A=⎣⎢⎢⎡426342263⎦⎥⎥⎤,X=⎣⎢⎢⎡xyz⎦⎥⎥⎤,B=⎣⎢⎢⎡609070⎦⎥⎥⎤
Here,
∣A∣=4(12−12)−3(6−36)+2(4−24)
⇒∣A∣=90−40=50
Since, ∣A∣=0
Hence, the system of equations is consistent and has a unique solution given by X==A−1B
A−1=∣A∣adjA
Answer:
Shipping company IPS has shipping rates that are a function of the weight of the parcel. For packages weighing less than or equal to 5 pounds, they charge $ 1 per pound. For packages weighing between 5 and 10 pounds, they charge $ 2 per pound. If packages weigh 10 pounds or more, they charge $ 2.75 per pound. IPS refuses to ship any parcel weighing more than 51 pounds. There is also a flat fee of $ 1 for all deliveries and an additional fee of $ 3 for all deliveries weighing 10 pounds or more.
Complete the following description of a piecewise function so that it describes the shipping costs C(x) in dollars as a function of the weight x in pounds.
C(x)= {... if x is in the interval ...
{... if x is in the interval ...
{... if x is in the interval ...