nZ carbon and coal #1
using equations and desmos
OK guys so we now go back to the beginning with our carbon and coal activity. Remember this is the example where there was a limit of 8 trips per train.
1) NZ COAL AND CARBON version 1
NZ coal and carbon uses two freight trains to deliver coal and timber to their depot.
Train A can carry 2 Tonnes of coal and 1/2 Tonne of timber per trip.
Train B can carry 1 Tonne of coal and 1 Tonnes of timber per trip.
Each day the trains need to deliver at least 10 Tonnes of coal and 7 Tonnes of timber.
The maintenance crew has told management that the trains cannot make any more than 8 trips per day (each train)
Calculate the number of trips both trains need per day to minimize fuel costs in a written report.
The fuel cost equation is C= 360x + 240y
the graphs for carbon and coal in desmos
Adding more detail to the graph
wrap up video (almost) for merit -
what the report part will look like
x ≤ 8= trips with train A ( oops, not mentioned in video the ≤ symbol needs to be there!)
y ≤ 8= trips with train B
2x + y ≥ 10 for trips with coal
1/2x + y ≥ 7 for trips with timber
A(1,8) cost = 360 x 1 + 240 x 8 = $2280
B(8,7) cost = 360 x 8 + 240 x 8 = $4800
C(8,3) cost = 360 x 8 + 240 x 3 = $3600
D(2,6) cost = 360 x 2 + 240 x 6 = $2160
The point that minimises fuel costs is D(2,6)
To minimise the fuel costs, NZ Carbon and coal should run 2 trips a day for train A and 6 trips a day for train B. The daily fuel cost is at a minimum of $2160
And for High Merit:
From the increased fuel cost equation of F = 500x + 250y
A(1,8) cost = 500 x 1 + 250 x 8 = $2500
B(8,7) cost = 500 x 8 + 250 x 8 = $6000
C(8,3) cost = 500 x 8 + 250 x 3 = $4750
D(2,6) cost = 500 x 2 + 250 x 6 = $2500
The company now has two options that give the lowest fuel cost. It can either run 1 trip with train A and 8 trips with train B each day or 2 trips with train A and 6 trips with train B each day. The minimum cost is $2500. That takes it to high Merit.
part 2 for excellence
monday 18th may
The cost of production changes such that the new income/cost equation is
F = 500x + 250y
How does the increase in costs affect the number of trips the freight trains can take?
F = 500x + 250y
How does the increase in costs affect the number of trips the freight trains can take?