Optimum profit per p_fail
(measured over 15 replications at the optimal α × β × n_backup)

p_fail	α*	β*	n_backup*	Profit (Cr/day)
0.005 (200 d)	0.8	0.3	2	63.76
0.01 (100 d)	0.9	0.3	2	61.14
0.02 (50 d)	0.9	0.9	2	56.89

Marker color = retailer's mean simulated profit/day,
on one shared color scale across the three p_fail layers.