Question

SURVEY SAMPLING. Gladstone and Associates is conducting a survey of 2000 investors for the financial advising firm of William and Ryde to determine satisfaction with their services. The investors are to be divided into four groups:

Group I: Large investors with William and Ryde Group II: Small investors with William and Ryde Group III: Large investors with other firms Group IV: Small investors with other firms

The groups are further subdivided into those that will be contacted by telephone and those that will be visited in person. Due to the different times involved in soliciting information from the various groups, the estimated cost of taking a survey depends on the group and method of survey collection. These are detailed in the following table.

	Survey Costs
Group	Telephone	Personal
I	$15	$35
II	$12	$30
III	$20	$50
IV	$18	$40

Determine the number of investors that should be surveyed from each group by telephone and in person to minimize Gladstone and Associates’ overall total estimated cost if:

- At least half of those surveyed invest with William and Ryde.

- At least one-fourth are surveyed in person.

- At least one-half of the large William and Ryde investors surveyed are contacted in person.

- At most 40% of those surveyed are small investors.

- At least 10% and no more than 50% of the investors surveyed are from each group.

- At most 25% of the small investors surveyed are contacted in person.

Answer 1

The problem formulated using a Linear Programming model with decision variables solved in Excel using LP SOLVER is shown below:

Formulae used:

SOLVER parameters used:

The ones highlighted in blue are Decision Variables. The one in Yellow is the Target Function that is to be minimized.

Variable Notation:

Lwr_Tel = No. of Large Investors with William and Ryde contacted by Telephone;

Lwr_Per = No. of Large Investors with William and Ryde contacted in Person;

Swr_Tel = No. of Small Investors with William and Ryde contacted via Telephone;

Lothers_Per = No. of Large Investors with Other firms contacted in Person and likewise.

Table form is also given below for better clarity:

						Costs			Constraint (e)
Decision Variables	Group	Telephone	Personal	# by Telephone	# by Personal	Telephone Costs	Personal Costs		Group_L		Per Group		Group_U
LWR_Tel , LWR_Per	1	$15	$35	500	500	$7,500	$17,500		200	<=	1000	<=	1000
SWR_Tel , SWR_Per	2	$12	$30	600	0	$7,200	$0		200	<=	600	<=	1000
LOthers_Tel , LOthers_Per	3	$20	$50	200	0	$4,000	$0		200	<=	200	<=	1000
SOthers_Tel , SOthers_Per	4	$18	$40	200	0	$3,600	$0		200	<=	200	<=	1000
					2000	Total Cost =	$39,800
					=
					2000
Constraints:
(a)	1600	>=	1000	LWR_Tel + LWR_Per + SWR_Tel + SWR_Per >= 1000
(b)	500	>=	500	LWR_Per + SWR_Per + LOthers_Per + SOthers_Per >= 500
(c)	500	>=	500	LWR_Per >= LWR_Tel
(d)	800	<=	800	SWR_Tel + SWR_Per + SOthers_Tel + SOthers_Per >= 40%*2000
(e)	Above
(f)	0	<=	200	SWR_Per + SOthers_Per <= 25%*(SWR_Tel + SWR_Per + SOthers_Tel + SOthers_Per)