Graph C is the correct representation of the solution set to the system of inequalities.
The two inequalities that represent this situation are:
Number of copies: He needs to print at least 6 copies, so the total number of copies (color + black and white) must be greater than or equal to 6. This can be written as:
Color copies + Black and white copies ≥ 6
Time constraint: He has 12 minutes to print all the copies. Since a color copy takes 3 minutes and a black and white copy takes 1 minute, the total printing time must be less than or equal to 12 minutes. This can be written as:
3 * Color copies + 1 * Black and white copies ≤ 12
Now, let's analyze the graphs:
Graph A: This graph shows the feasible region for the inequality Color copies + Black and white copies ≥ 6. The shaded area represents all the combinations of color and black and white copies that satisfy this inequality. However, it doesn't take into account the time constraint.
Graph B: This graph shows the feasible region for the inequality 3 * Color copies + 1 * Black and white copies ≤ 12. The shaded area represents all the combinations of color and black and white copies that satisfy this time constraint. However, it doesn't take into account the minimum number of copies required.
Graph C: This graph correctly represents the solution set to the system of inequalities. It shows the intersection of the shaded areas from graphs A and B. This intersection represents all the combinations of color and black and white copies that satisfy both the minimum number of copies requirement and the time constraint.
Therefore, Graph C is the correct representation of the solution set to the system of inequalities.