Question

A marketing research firm has been retained to conduct focus group interviews for a real estate company. Plans are made to classify the participants into () over-45 or not; and (i) whether they have recently bought or sold a house or not. X11 =number of participants who are over-45 and are recent buyer or seller; X12 = number of participants who are over-45 and are not recent buyer or seller, X21 =number of participants who are 45-or-under and are recent buyer or seller; X22 = number of participants who are 45-or-under and are not recent buyer or seller. Specific guidelines are: (1) At least 200 people must be selected; (2) At least 10% of all participants must have bought or sold recently; (3) At least 40% of those who have not bought or sold recently must be over-45; (4) At least 40% of all participants must be 45-or-under. One of the following constraints is NOT correct: (Hints: Note the + or - signs) Select one: O a. .90x11 + 10x12 + 90X21 - 10/22 2 0; O b. 60x12 - 140x22 0; O c.-.40X11 - 40x12 + .60X21+ .60X220; O d. X11 + X12 + x21 + X22 200.

Answer 1

Tabular representation of the variables: Over-45 45-or-under Recent Buyer or seller X11 X21 Not a Recent Buyer or seller X12 X22 Constraint 1: X11+ X12 + X21+ X22 200 Constraint 2: X11+X12 2 0.1 (X11 + X12 + Xz1+X22) Rearranging we get, 0.9*X11+0.9*X12-0.1*X21 -0.1*X2220 Constraint 3: X12 2 0.4 (X12 + X22) Rearranging we get, 0.6*X12 - 0.4*X2220 Constraint 4: X21 + X22 20.4 (X11 + X12+ X21 + X22) Rearranging we get, 0.6*X21 +0.6*X22-0.4*X11-0.4*X1220 Question 1: Option a is wrong as the correct representation is as shown in the constraint 2 above.

Question 2: The objective is to minimize the total cost. Screening Cost Additional contact cost X11 10 X12 10 X21 10 10 10 10 Additional time cost 5 Total Cost 10 15 20 25 X22 5 OF = Min 10* X11 + 15*X22 + 20*X21 + 25*X22 Hence Option a is correct Question 3: Option d is false as a feasible decision should satisfy all the constraints and not just at least one.