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 the overall equation represented by this scenario (all points may not apply to the scenario)?

On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (1, negative 1). Everything to the right of the line is shaded.
On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (1, negative 1). Everything to the left of the line is shaded.
On a coordinate plane, a solid straight line has a negative slope and goes through (0, 3) and (1, negative 1). Everything to the right of the line is shaded.
On a coordinate plane, a solid straight line has a negative slope and goes through (0, 3) and (1, negative 1). Everything to the left of the line is shaded.

Answer 1

Let x = time for the repeated process and y = time for the single process. The cycle constraint is 4x + y ≤ 3.

So the boundary line is y = 3 − 4x (goes through (0,3) and (1,−1)), it should be solid (≤), and the region satisfying the inequality includes (0,0). Therefore the correct graph is: the solid line through (0,3) and (1,−1) with everything to the left of the line shaded (option 4).