market survey inc MSI specializes in evaluating consumer rea

market survey inc. (MSI) specializes in evaluating consumer reaction to new products. Alcient has recently asked MSI to conduct 1000 door-to-door personal interview to obtain response fom household iwht childre and households without children to a new product. MSI can do both day and evening interviews with the following cost per interview:

Interview at least 300 evening interviews

At least 40% of the day interviews must be from households with children; Find the optimal number of interviews of each type?

Solution

Day interviews with children: x

Day interviews without children: y

Evening interviews with children: z

Evening interviews without children:w

Minimise: 20x+18y+25z+20w

Such that

x>=0

y>=0

z>=0

w>=0

x+y+z+w = 1000

z+w>=300

x<=0.4(x+y) or 0.6x-0.4y<=0

Solving this problem using the simplex method we get:

Optimal Solution: Cost = 19160; x = 280, y = 420, z = 0, w = 300