Question

English Motors, Ltd. (EML), developed a new all-wheel-drive sports utility vehicle. As part of the marketing campaign, EML produced a video tape sales presentation to send to both owners of current EML four-wheel-drive vehicles as well as to owners of four-wheel-drive sports utility vehicles offered by competitors; EML refers to these two target markets as the current customer market and the new customer market. Individuals who receive the new promotion video will also receive a coupon
 for a test drive of the new EML model for one weekend. A key factor in the success of the new promotion is the response rate, the percentage of individuals who receive the new promotion and test drive the new model. EML estimates that the response rate for the current customer market is 25% and the response rate for the new customer market is 20%. For the customers who test drive the new model, the sales rate is the percentage of individuals that makes a purchase. Marketing research studies indicate that the sales rate is 12% for the current customer market and 20% for the new customer market. The cost for each promotion, excluding the test drive costs, is $4 for each promotion sent to the current customer market and $6 for each promotion sent to the new customer market. Management also specified that a minimum of 30,000 current customers should test drive the new model and a minimum of 10,000 new customers should test drive the new model. In addition, the numbers of current customers who test drive the new vehicle must be at least twice the number of new customers who test drive the new vehicle. If the marketing budget, excluding test drive costs, is $1.2 million, how many promotions should be sent to each group of customers in order to maximize total sales?

Answer 1

Let       C = number sent to current customers

            N = number sent to new customers

 

Number of current customers that test drive = .25 C 

Number of new customers that test drive = .20 N

 

Number sold   =  .12 (.25 C) + .20 (.20 N)

                        =  .03 C + .04 N

  

                                                                                 

Max	.03C	+	.04N
s.t.
	.25 C			≥	30,000	Current Min
			.20 N	≥	10,000	New Min
	.25 C	-	.40 N	≥	0	Current vs. New
	4 C	+	6 N	≤	1,200,000	Budget

                                     C, N, ≥ 0