M3_A5. A political polling organization has been hired toconduct a poll of likely voters prior to an upcoming election. Eachvoter is to be interviewed in person. It is known that he costs ofinterviewing different types of voters vary due to the differencein proportion within the population. The costs to interview males,for example, are $20 per Democrat, $18 per Republican, and $27 perIndependent voter. The costs to interview female are $24, $22 and$28 for Democrat, Republican, and Independent voters, respectively.The polling service has been given certain criteria to which itmust adhere: ? There must be at least 7,500 total interviews. ? Atleast 2,500 independent voters must be polled ? At least 3,800males must be polled. ? At least 3,250 females must be polled ? Nomore than 35% of those polled may be Democrats ? No more than 35%of those polled may be Republicans ? No more than 15% of thosepolled may be Republican males. ? Each of the six types of votersmust be represented in the poll by at least 13% of the totalinterviews Formulate and solve this problem in Excel to determinethe number of each type of voter that meets the requirements andminimize the cost to carry out the interviews. a) How many decisionvariables does this problem have? b) Not counting thenon-negativity constraint - how many constraints does this problemhave? c) What is the minimum cost in your optimal solution (thevalue of the objective function)? d) Based on your solution – howmany Democrat Males should be interviewed? e) Based on yoursolution – how many Republican Males should be interviewed? f)Based on your solution – how many Independent Males should beinterviewed? g) Based on your solution – how many Democrat Femalesshould be interviewed? h) Based on your solution – how manyRepublican Females should be interviewed? i) Based on your solution– how many Independent Females should be interviewed?
