Answer:
The last graph in the option represents the overall equation of this scenario (it is option D if the last graph shown is the fourth option).
Step-by-step explanation:
A manufacturing machine has two processes.
First let's represent the time of the two processes with variables:
The time of 1st process = a
The time of 2nd process = b
Since 1st process is repeated 4 times = 4×a = 4a
Also 2nd process is repeated only once = 1×b = b
Then we would represent the equation of the entire process
The entire cycle is said not to take longer than 3 minutes, meaning it less than or equal to 3 = ≤3
The equation of the entire process gives an inequality:
4a+b ≤ 3
Next, we would derive values for a to get b and vice versa in order to plot the graph using the equation: 4a+b = 3
For a = 0
4(0) +b= 3
b = 3
(a,b) = (0,3)
For b = 0
4a + 0 = 3
a= 3/4 = 0.75
(a,b) = (0.75, 0)
Let (a,b) represent (x,y) on the graph
Plotting the graph with coordinates (a,b) = (x,y) : (0,3), (0.75, 0); we get a line going downward passing, through 3 on y axis and 0.75 on x axis. The shaded portion represent the inequality: 4a+b ≤ 3
The last graph in the option represents the overall equation of this scenario (it is option D if the last graph shown is the fourth option).