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Lush Lawns, Inc. provides a lawn fertilizer and weed control service. They are adding a special aeration treatment as a low-cost extra service option, which it hopes will help attract new customers. Management is planning to promote this new service in two media: radio and direct-mail advertising. A budget of $2000 is to be used on this promotional campaign over the next quarter. Based on past experience in promoting its other services, Lush Lawns has been able to obtain an estimate of the relationship between sales and the amount spent on promotion in these two media:
s = 2x12 - 10x22 - 2x1x2 + 18x1 + 34x2
s.t. x1 + x2 = 2
Answer: x1 = 1.66; x2 = 0.33, Lagrange multiplier = 24
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