Question

A manufacturing machine has two processes. One of them is repeated 4 times and the second only once. The entire cycle can take no longer than 3 minutes. Which graph represents this scenario?

Answer 1

Answer:

The graph in the attached figure

Step-by-step explanation:

Let

x -----> time of the first process in minutes

y -----> time of the second process in minutes

we know that

The time of the first process multiplied by 4 (because is repeated 4 times) plus the time of the second process multiplied by 1 (because is repeated only once) must be less than or equal to 3 minutes

so

The inequality that represent this situation is

$4x+y\leq 3$

The solution of the inequality is the shaded area below the solid line

The equation of the solid line is $4x+y=3$

The y-intercept of the solid line is the point (0,3)

The x-intercept of the solid line is the point (0.75,0)

The slope of the solid line is negative m=-4

using a graphing tool

The solution is the shaded area

The graph in the attached figure

Remember that the time cannot be a negative number

Answer 2

Answer:

The inequality represents the situation is:

$4x+y\leq 3$

And the graph is attached in the solution.

Step-by-step explanation:

Given information:

Time of first process in minutes$=x$

Time of second process in minutes $=y$

As we know that ,

according to the given information in the question we can write:

the inequality represents the situation is:

$4x+y\leq 3$

Here, the y-intercept of the solid line is the point (0,3)

And the x-intercept of the solid line is the point (0.75,0)

And the slope is negative $m=-4$

Now the graph of the above inequality can be formed as attached in the solution:

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