A program is required to calculate the cost of a plumber$$s visit. If it is a non$-$urgent job, a plumber charges a $100$ call out fee that also covers the first hour $(60$ minutes$)$ of work. Each whole hour, or part of an hour, after that is charged at $50.$ However, if it is an urgent job, the call out fee $($that covers the first hour$)$ is $200$ and each hour or part of an hour after that is charged at $80.$

So$,$ for example, if the plumber takes $183$ minutes to complete an urgent job, the first $60$ minutes costs $200.$ The remaining $123$ minutes cost $240$ as there are $2$ complete hours and then part of an hour, which are each charged at $80,$ making a total bill of $440.$ For the same number of minutes for a non$-$urgent job, the total bill is $100$ for the call out and $150$ for the hours and part hour, so the total bill is $250.$

You are given part of the test data $($Table $3)$ and an error$-$filled program $($this can be downloaded from the assessment page$).$

Table $3$

Test number Input minutes urgent Expected output

$1119$ True $280$

$2120$ True $280$

$3121$ True $360$

$4119$ False $150$

$5120$ False $150$

$6121$ False $200$

# Problem: Calculate plumber$$s bill.

# Input: minutes worked

# Input: True if urgent, False otherwise

# Output: cost

minutes $=61$

urgent $=$ False

cost $=0$

hours $=1$

if minutes $>60$ :

hours $=$ minutes $//60$

if minutes $\%60==0$ :

hours $=$ minutes $//601$

if urgent

cost $=200+$ hours $*80$

if not urgent:

cost $=100+$ hours $*50$

print$($cost$)$

c$.$

i$.$Explain, in ordinary English, what the purpose of the first if statement is and how this is achieved in the Python code.

ii$.$This program is currently based on Pattern $4\mathrm{.}3.$ Explain why Pattern $4\mathrm{.}2$ would be better at expressing the last two multiple cases.

iii.Using Pattern $4\mathrm{.}2$ write an algorithm for this scenario. Your algorithm must initialise minutes and urgent to admissible values.

d$.$This part of the question involves writing Python code. Produce code corresponding to your algorithm. Include comments. Use the test table to check your code works. You do not need to submit test outputs.