*12. Sunray Electric Coop uses a fleet of 20 trucks to service its electric network. The company wants to develop a schedule of periodic preventive maintenance for the fleet. The probability of a breakdown in year 1 is zero. For year 2, the breakdown probability is .03, and it increases annually by .01 for years 3 through 10. Beyond year 10, the breakdown probability is constant at .13. A random breakdown costs $200 per truck, and a scheduled maintenance costs only $75 per truck. Sunray wants to determine the optimal period (in months) between scheduled preventive maintenances.

(a) Develop the associated decision tree.

(b) Determine the optimal maintenance-cycle length.