Answer to Question #259591 in Calculus for Alunsina

Question

A remittance company charges its customers based on the delivery rate table as shown. Amount is in Philippine peso.

Destination 1kg (max) 3kg (max) 5kg (max) 10kg (max) 20kg (max)

NCR 120 160 220 420 820

Luzon 150 190 320 620 1220

Mindanao 150 190 370 720 1420

(a) Write a rule of a piecewise-defined function C such that C(x) is the charge due on a weight x kg for NCR.

(b) Graph the function in (a)

(c) Use the table to find C (12.3) in Mindanao

(d) Use the table to find C(2.2) in Luzon

Answer 1

(a)

Piecewise defined function is given as follows:

$C(x) = \begin{cases} 120, 0< x\le1\\ 160, 1<x\le3 \\ 220, 3<x\le5\\ 420, 5<x\le10\\820, 10<x\le20 \end{cases}$

(b) The graph is

(c) From the graph

we find the value of C(12.3) in Mindanao.

Reading from the graph above at 12.3 we obtain

C(12.3)=1420 Philippine peso

(d)From the graph

We have to find the value of C(2.2) in Luzon

According to the graph we get C at 2.2

C(2.2)= 190 Philippine peso.