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 (i) over-45 or not; and (ii) whether they have recently bought or sold a house or not. X11 Enumber of participants who are over-45 and are recent buyer or seller; Xq2 = 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 - 10X22 2 0; O b..60x12 - .40X22 2 0; O c.-40X11 - .40X12 + .60X21 +.60X22 = 0; O d. X11 + X12 + X21 + X22 - 200.

Answer 1

ANSWER:

As per given guidelines

1)

At least 200 people must be selected

Formulation : x_{11 +} x_{12 +} x_{21 +} x_{22 ≥} 200 (option d)

2)

At least 10% of all participants must have bought or sold recently

x₁₁+x₂₁ >= 0.1*(x₁₁ + x₁₂ + x₂₁ + x₂₂)
or, 0.9x₁₁-0.1x₁₂+0.9x₂₁-0.1x₂₂ >= 0 (option a)

3)

At least 40% of those who have not bought or sold recently must be over-45

x₁₂ >= 0.4(x₁₂+x₂₂)

or, 0.60x₁₂-0.40x₂₂ >= 0 (option b)
4)

At least 40% of all participants must be 45-or-under

x₂₁+x₂₂ >= 0.4*(x₁₁ + x₁₂ + x₂₁ + x₂₂)
or, -0.4x₁₁-0.4x₁₂+0.6x₂₁+0.6x₂₂ >= 0 (option c)

So, Constraint described in 'options c' is incorrect.

............................................

Given

screening cost = $10

additional contact adds to the cost = $10

additional time adds another to the cost = $5

total cost became $10 + $5 = $15

each participant 45 or under

The OF is:

Min 10x₁₁ + 15x₁₂ + 20x₂₁ + 25x₂₂

(option - a)

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