Question

For a telephone survey, a marketing research group needs to contact at least 100 national private companies, 85 international private companies, 60 national public companies, and 30 international public companies. It costs $1.5 to make a daytime call and (because of higher labor costs) $2.5 to make an evening call. The following Table lists the results. Based on the results of a LP model, what is the most efficient way of completing the survey?

Company	Percent of	Percent of
Responding	Daytime Calls	Evening Calls
national private companies	10	30
international private companies	20	30
national public companies	40	20
international private companies	20	15
none	10	5

Answer 1

Let the total no. of daytime calls be “x” and total no. of evening calls be “y”. These are the decision variables.

Objective function = Total cost = 1.5x+2.5y. This has to be minimized.

Constraints:

(1) 0.1x+0.3y>=100 (at least 100 national private companies)

(2) 0.2x+0.3y>=85 (85 international private companies)

(3) 0.4x+0.2y>=60 (60 national public companies)

(4) 0.2x+0.15y>=30 (30 international public companies)

(5) x,y>=0 (non negativity).

(6) x,y = integers (as no. of calls cannot be negative)

Solving in excel, using the solver function, we get:

	Total no. of daytime calls	1.00
	Total no. of evening calls	333.00
				Formula
	Objective function	834.00		1.5x+2.5y
	Constraints
1	100.00	>=	100.00	0.1x+0.3y>=100
2	100.10	>=	85.00	0.2x+0.3y>=85
3	67.00	>=	60.00	0.4x+0.2y>=60
4	50.15	>=	30.00	0.2x+0.15y>=30

Thus no. of daytime calls = 1 and no. of nighttime calls = 333.

Minimized cost = $834. All constraints are satisfied.