sand and deliver (practice 5)
Able, Baker and Charley are small landscape suppliers that deliver sand and cement for their DIY customers. Their delivery charges do not include the cost of the sand or cement and are not part of this assessment.
Represent each company's charge as an equation.
Able C = 2D + 10
Baker C = 3.4D + 3
Charley C = 30
Baker C = 3.4D + 3
Charley C = 30
represent each company's charges in a graph.
at which distance do Able and Baker cost the same and why?
Able and Baker cost the same at a distance of 5 km. The cost is $20. This is the point where the two graphs intersect (at the point (5,20))
For a higher grade solve a pair of simultaneous equations:
3.4D + 3 = 2D + 10
3.4D - 2D = 10 - 3
1.4D = 7
D = 5 km, so Able and Baker cost the same at a distance of 5 km. The cost is $20.
This is the point where the two graphs intersect.
For a higher grade solve a pair of simultaneous equations:
3.4D + 3 = 2D + 10
3.4D - 2D = 10 - 3
1.4D = 7
D = 5 km, so Able and Baker cost the same at a distance of 5 km. The cost is $20.
This is the point where the two graphs intersect.
which company is cheapest to Allerton?
Looking at my table the cheapest company to Allerton is Baker, It costs $16.60 and this is $1.40 cheaper than Able. However, it would be cheaper to use Able to go to Blueweed at $22, $1.40 cheaper than Baker.
what range of distances would be cheapest to use Able and why?
Looking at my graph, I can see it would be cheaper to use Able's over 5 km and up to 10 km. Thats because between 5 and 10 km its line is lower than the other graphs.
Able wants to be the cheapest company
Able can keep the same slope as Baker but have a lower fixed charge say $2. So their charge equation will be Cost = 3.4D + 2 This could be achieved up to about 8 km. Able can then stay below Charley's flat rate of $30 by charging $29 so Able's new charge would be a flat rate of C = 29 for distances greater than 8 km up to 50 km. Able would be the cheapest but only up to 50 km. We don’t know what Charley's charges are above 50 km but Able could adjust their charges to compete with Charley's.
Alternatively, Able could use a step charge (series of flat rates) that charges in stages. For example, from 0 km up to 3 km they could charge $2, (C = 2)
3 km up to 6 km - C = 15
6 km up to 8 km - C = 22
above 8 km and up to 50 km $29 or C = 29
New graphs shown in green below.
3 km up to 6 km - C = 15
6 km up to 8 km - C = 22
above 8 km and up to 50 km $29 or C = 29
New graphs shown in green below.