Market research survey. Market Surveys, Inc. specializes in evaluating consumer

Question

Market research survey. Market Surveys, Inc. specializes in evaluating consumer reac tion to new products, services, and/or advertising campaigns. A client has just asked Mar. ket Survey to provide information on consumer reaction to a recently marketed new prod uct. The client's contract calls for a door-to-door, personal interview survey with the following stipulations: 1. Survey at least 400 households with children. 2. Survey at least 200 households with no children. 3. The total number of households contacted during the evening should be at least as great as the number contacted during the day. 4. The total sample must be at least 1000 households. Based upon previous interviews, management has developed the following interview costs: Day Household Children No children Interview Cost Evening S10 S12 S 8 S10

Explanation / Answer

Since X2 is 500 and all the calculations will be based on this in order to achieve minimum cost following all the terms given in the question then x4 will be 0 because of the condition of equal households should be contacted day and evening out of 1000.

So x2= 500

x 4= 0

So X2= 500 and total of X1 and X3 should be 400 which means the total X4 is 100 households with no children.

Now x2 means 500*$8 = $4000

x4 means 0 = 0

Total number of household with no children in a day is 4000+0= $4000........a

Now to get the minimum cost if x1= 400*$10= $4000 as minimum 400 household should be surveyed with children

and x3 means no children houseday in day remaining = 100*$8= $800

So total of x1 and x3 = 4000+800= $4800.....b

So for 1000 surveys the minimum total cost will be a+b= 4000+4800= $8800

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