Question

XYZ Company is pianning an advertising campaign for its new product. The mediaconsidered are television and radio. Rated exposures per thousand dollars of advertisingexpenditure are 10,000 for TV and 7,500 for radio. Management has agreed that thecampaign cannot be judged successful it total exposures are under 750,000. The campaignwould be viewed as superbly successful if 1 million exposures occurred. In addition, thecompany has realized that the two most important audiences for its product are persons 18 to21 years of age and persons 25 to 30 years of age. The following table estimates the numberof individuals in the two age groups expected to be exposed to advertisements per $1,000 ofexpenditures:4. Management has rank ordered five goals it wishes to achieve, arranged from highest to lowestpriorities. 1. Achieve total exposures of at least 750,000 persons. 2. Avoid expenditures of more than $100,000. 3. Avoid expenditures of more than $70,000 for television advertisements. 4. Achieve at least 1 million total exposures. 5.. Reach at least 250,000 persons in each of the two age groups, 18-21 and 25-30 years. Inaddition, management realizes and wishes to account for the fact that the purchasing powerof the 25-30 age group is twice that of the 18-21 age group. a. Formulate the above problem as a linear goal program. p. What modification is necessary in the formulation if the purchasing power differential is to be ignored? c. Does the number of goal constraints always equal the number of goals? d. Suppose the management specifies a goal of keeping budget overruns for thecampaign below $5,000. Ässume this goal to have the second highest priority,with goals 2-5 in the öriginal formulation becoming goals 3-6. With respect to part (i) appropriately modify the objective function Z. (ii) add a goal constraint exclusively in terms of deviational variables. (iii) rewrite (ii) using only the decision variable.

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