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MARKETING AND MEDIA APPLICATIONS 167

Interview Cost
Household Day Evening
Children E20 E25
No children E18 E20

What is the household, time-of-day interview plan that will satisfy the contract
requirements at a minimum total interviewing cost?
In formulating the linear programming model for the MSI problem, we utilize the
following decision-variable notation:

DC ¼ the number of daytime interviews of households with children
EC ¼ the number of evening interviews of households with children
DNC ¼ the number of daytime interviews of households without children
ENC ¼ the number of evening interviews of households without children
We begin the linear programming model formulation by using the cost-per-interview
data to develop the objective function:
Min 20DC þ 25EC þ 18DNC þ 20ENC
The constraint requiring a total of 1000 interviews is:

DC þ EC þ DNC þ ENC ¼ 1000
The five specifications concerning the types of interviews are as follows.
l Households with children:

DC þ EC 400
l Households without children:

DNC þ ENC 400

l At least as many evening interviews as day interviews:
EC þ ENC DC þ DNC

The usual format for linear programming model formulation and computer input
places all decision variables on the left side of the inequality and a constant (possibly
zero) on the right side. Thus, we rewrite this constraint as:

DC þ EC DNC þ ENC 0
l At least 40 per cent of interviews of households with children during the evening:

EC 0:4ðDC þ ECÞ or 0:4DC þ 0:6EC 0

l At least 60 per cent of interviews of households without children during the
evening:

ENC 0:6ðDNC þ ENCÞ or 0:6DNC þ 0:4ENC 0
When we add the nonnegativity requirements, the four-variable and six-constraint
linear programming model becomes:

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