Market Pulse Research Has Conducted a Study for Lucas Furniture

Question

Examlex · Accepted Answer

The Answer is Define the decision variables:
There are

7 l _ { i j }

decision variables, one for each level of attribute.

l _ { i j } = 1

if Lucas chooses level

i

for attribute

j ; 0

otherwise.
There are

7 Y _ { k }

decision variables, one for each consumer in the sample.

Y _ { k } = 1

if consumer

k

chooses the Lucas brand, 0 otherwise.

Define the objective function:
Maximize the number of consumers preferring the Lucas brand desk.

\operatorname { Max } \quad Y _ { 1 } + Y _ { 2 } + Y _ { 3 } + Y _ { 4 } + Y _ { 5 } + Y _ { 6 } + Y _ { 7 }

Define the constraints:
There is one constraint for each consumer in the sample.

\begin{array} { c } 5 l _ { 11 } + 26 l _ { 21 } + 20 l _ { 31 } + 18 l _ { 12 } + 11 l _ { 22 } + 17 l _ { 13 } + 10 l _ { 23 } - 50 Y _ { 1 } \geq 1 \18 l _ { 11 } + 11 l _ { 21 } + 5 l _ { 31 } + 12 l _ { 12 } + 16 l _ { 22 } + 15 l _ { 13 } + 26 l _ { 23 } - 50 Y _ { 2 } \geq 1 \4 l _ { 11 } + 16 l _ { 21 } + 22 l _ { 31 } + 7 l _ { 12 } + 13 l _ { 22 } + 11 l _ { 13 } + 19 l _ { 23 } - 50 Y _ { 3 } \geq 1 \12 l _ { 11 } + 8 l _ { 21 } + 4 l _ { 31 } + 18 l _ { 12 } + 9 l _ { 22 } + 22 l _ { 13 } + 14 l _ { 23 } - 50 Y _ { 4 } \geq 1 \19 l _ { 11 } + 9 l _ { 21 } + 3 l _ { 31 } + 4 l _ { 12 } + 14 l _ { 22 } + 30 l _ { 13 } + 19 l _ { 23 } - 50 Y _ { 5 } \geq 1 \6 l _ { 11 } + 15 l _ { 21 } + 21 l _ { 31 } + 8 l _ { 12 } + 17 l _ { 22 } + 20 l _ { 13 } + 11 l _ { 23 } - 50 Y _ { 6 } \geq 1 \9 l _ { 11 } + 6 l _ { 21 } + 3 l _ { 31 } + 13 l _ { 12 } + 5 l _ { 22 } + 16 l _ { 13 } + 28 l _ { 23 } - 50 Y _ { 7 } \geq 1\end{array}

There is one constraint for each attribute.

\begin{array} { l } l _ { 11 } + l _ { 21 } + l _ { 31 } = 1 \l _ { 12 } + l _ { 22 } = 1 \l _ { 13 } + l _ { 23 } = 1\end{array}

Optimal Solution:
Lucas should choose these product features:

1 file drawer

\left( I _ { 21 } = 1 ight)

No pullout writing boards

\left( I _ { 22 } = 1 ight)

Simulated wood finish

\left( I _ { 13 } = 1 ight)

Three sample participants would choose the Lucas design:
Participant

1 \left( Y _ { 1 } = 1 ight)

Participant

5 \left( Y _ { 5 } = 1 ight)

Participant

6 \left( Y _ { 6 } = 1 ight)

Definitions: