11 A grocery chain wants to promote the sale of a new flavor of ice cream by issuing up to 15,000 coupons by mail to preferred customers. The budget for this promotion has been limited to $12,000.

The following table shows the expected increased sales per coupon and the probability of coupon usage for the various coupon amounts under consideration.

COUPON AMOUNT INCREASED SALES PER COUPON

(CARTONS)

PROBABILITY COUPON WILL BE USED

$1.00 1.50 0.80

$0.85 1.40 0.75

$0.70 1.25 0.60

$0.55 1.00 0.50

$0.40 0.90 0.42 For example, every $1-off coupon issued will stimulate sales of 1.5 additional cartons. However, since the probability that a $1-off coupon will actually be used is only 0.80, the expected increased sales per coupon issued is 1.2 1= 0.8 * 1.52 cartons.

The selling price per carton of ice cream is $3.50 before the coupon value is applied. The chain wants at least 20% of the coupons issued to be of the $1-off variety and at least 10% of the coupons issued to be of each of the other four varieties. What is the optimal combination of coupons to be issued, and what is the expected net increased revenue from this promotion?