Honey is a technology company that provides online coupons to its subscribers. Honey's analytics staff has developed a classification method to predict whether a customer who has been sent a coupon will apply the coupon toward a purchase. For a sample of customers, the following table lists the classification model's estimated coupon usage probability for a customer. For this particular campaign, suppose that when a customer uses a coupon, Honey receives $1 in revenue from the product sponsor. To target the customer with the coupon offer, Honey incurs a cost of $0.05. Honey will offer a customer a coupon as long as the expected profit of doing so is positive. Using the equation

Expected Profit of Coupon Offer = P(coupon used) × Profit if coupon used + (1 - P(coupon used)) × Profit if coupon not used

determine which customers should be sent the coupon.

Customer Probability of Using Coupon
1 0.47
2 0.35
3 0.27
4 0.03
5 0.08
Determine the expected profit for each customer. Round your answers to the nearest cent. Enter negative value as negative number, if any.

Customer Expected Profit
1 $
2 $
3 $
4 $
5 $
The expected profit is positive for customers
- Select your answer -
, so these customers
- Select your answer -
the coupon

Respuesta :

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.

What is the expected profit for all customers?

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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