In a project requiring a total of 120 hours of work, you have three resources: Resource A, Resource B, and Resource C, with productivity rates of 5, 4, and 3 hours per day, respectively. If you allocate resources such that Resource A works for $x$ days, Resource B for $y$ days, and Resource C for $z$ days, which of the following allocations meets the requirement while minimizing the total number of days worked? a) $x = 12, y = 6, z = 0$ b) $x = 10, y = 5, z = 5$ c) $x = 8, y = 8, z = 4$ d) $x = 6, y = 10, z = 6$