Based on the expected profit to Honey, and the probability of the various customers using the coupons, all customers except customer 4 should be sent coupons.
The profit to Honey if people use the coupons is:
= Revenue - Cost
= 1 - 0.05
= $0.95
The profit if the coupon is not used is the cost of $0.05.
Customer 1 expected profit:
= P(coupon used) × Profit if coupon used + (1 - P(coupon used)) × Profit if coupon not used
= (0.47 x 0.95) + ( (1 - 0.47) x -0.05)
= $0.42
Customer 2 expected profit:
= (0.35 x 0.95) + ( (1 - 0.35) x -0.05)
= $0.30
Customer 3 expected profit:
= (0.27 x 0.95) + ( (1 - 0.27) x -0.05)
= $0.22
Customer 4 expected profit:
= (0.03 x 0.95) + ( (1 - 0.03) x -0.05)
= -$0.02
Customer 5 expected profit:
= (0.08 x 0.95) + ( (1 - 0.08) x -0.05)
= $0.03
In conclusion, all customers expect customer 4 should be sent the coupons as they result in profits.
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