Market Pulse Research has conducted a study for Lucas Furniture on some designs for a new commercial office desk. Three attributes were found to be most influential in determining which desk is most desirable: number of file drawers, the presence or absence of pullout writing boards, and simulated wood or solid color finish. Listed below are the part-worths for each level of each attribute, provided by a sample of seven potential Lucas customers.

	File Drawers	Pullout Writing Boards	Finish
Consumer	0	1	2	Present	Absent	Simulated Wood	Solid Color
1	5	26	20	18	11	17	10
2	18	11	5	12	16	15	26
3	4	16	22	7	13	11	19
4	12	8	4	18	9	22	14
5	19	9	3	4	14	30	19
6	6	15	21	8	17	20	11
7	9	6	3	13	5	16	28

Suppose the overall utility (sum of part-worths) of the current favorite commercial office desk is 43 for each customer. What product design will maximize the share of choices for the seven sample participants? (For the file drawers attribute, let i = 1, 2, 3 correspond to zero, one, and two drawers, respectively. For the pullout writing boards attribute, let i = 1, 2 correspond to present and absent, respectively. For the finish attribute, let i = 1, 2 correspond to simulated wood and solid color, respectively. Let j = 1, 2, 3 correspond to the file drawers, pullout writing boards, and finish attributes, respectively. Let L_ij = 1 if Lucas chooses level i for attribute j; 0 otherwise. Let Y_k = 1 if consumer k chooses the Lucas brand; 0 otherwise.)

Max

s.t.

consumer 1

consumer 2

consumer 3

consumer 4

consumer 5

consumer 6

consumer 7

file drawers

pullout writing boards

finish

L_ij, Y_k = 0, 1

Using Excel or other software, formulate and solve this 0-1 integer programming problem.

(L₁₁, L₂₁, L₃₁, L₁₂, L₂₂, L₁₃, L₂₃, Y₁, Y₂, ..., Y₇) = ( )