Question

The supervisor of a building project needs to organise waste collection for the duration of the project. In the local area there are two waste collection companies offering two different models of subscription and you are asked to determine which will be the best option financially. Bin-a-gogo offers each collection of rubbish at the cost of £209. We-Want-Your-Waste-Plc offers each collection of rubbish at the cost of £120, however there is a sign- up fee of £450

Answer 1

Solution: Below is the Data given as per Ques:

There are 2 waste collection companies named Bin-a-gogo & We-Want- Your-Waste-Plc offers 2 different models of subscription.

(a) Formula to calculate the total cost for a given number of collections:

(i) Total cost will be calculated by Bin-a -gogo using the below formula:

Number of collections of rubbish * cost of each collection of rubbish

(ii) Total cost will be calculated by We-Want-Your-Waste-Plc using the below formula:

Number of collections of rubbish * cost of each collection of rubbish + Sign -up fee

(b) Project lasted for 9 weeks and collections were made once per week

No. of collections in 9 weeks = 1/week * 9 weeks = 9 collections in 9 weeks

(i) Total Cost of collection by Bin-a-gogo = Number of collections of rubbish * cost of each collection of rubbish

                                                           = 9 collections * 209(in pounds)

    Cost of collection by Bin-a-gogo = 1881(pounds)

(ii) Total cost of collection by We-Want-Your-Waste-Plc = Number of collections of rubbish * cost of each collection of rubbish + Sign -up fee

                                                                                      = 9 collections * 120(pounds) + 450(pounds)

Total cost of collection by We-Want-Your-Waste-Plc = 1530 (pounds)

Therefore, Most cost-effective company is " We-Want-Your-Waste-Plc" as their total cost of collection is lower.

(c) As per the Graphical presentaion of total cost of collection both the companies, it is clear that when the number of collections are upto 5(i.e from 1 to 5) , then "Bin-a-gogo" is the cheapest company in terms of total cost of collection.

However, when the number of collections are more than 5 and upto 20(i.e. from 6 to 20), then the cheapest company in terms of total cost of colletion is " We-Want-Your-Waste-Plc"

Chart Title 4500 4000 3500 3000 2500 2000 1500 1000 500 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Total code (Bin-a-gigo) Total code(We-Want-Your-waste-PC)

Calculations for reference

No. of collections	Total cost( (Bin-a-gogo)	Total cost(We-Want-Your-waste-Plc)
1	209	570
2	418	690
3	627	810
4	836	930
5	1045	1050
6	1254	1170
7	1463	1290
8	1672	1410
9	1881	1530
10	2090	1650
11	2299	1770
12	2508	1890
13	2717	2010
14	2926	2130
15	3135	2250
16	3344	2370
17	3553	2490
18	3762	2610
19	3971	2730
20	4180	2850

(D) From the graph as provided in part (c), When the Number of collections are upto 5 (i,e, from 1 to 5), then "Bin-a-gogo" is the cheapest company and when the number of collections are more than 5, then "We-Want-Your-Waste-Plc" is the cheapest company in term of Total cost of collection.

Conclusion : Higher the number of collections, It is more beneficial for the "We-want-your-waste-Plc" in terms of total cost of collection as their cost will be lower as compared to "Bin-a- gogo"