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 process that repeats (each), y = time for the single process. The cycle time limit is

4x + y ≤ 3.

Rewrite as y = −4x + 3 for the boundary. Because the inequality is ≤, the boundary is a solid line, and the feasible region is the half-plane that contains (0,0) (since 4·0+0 ≤ 3).

The correct graph is the solid line through (0,3) and (1,−1) with the region to the right/including the origin shaded — option 3.