Question

A marketing research firm would like to do a survey for one of their clients. The survey is for a local newspaper that would like to know how effective its advertising strategy has been for a new publication. The cost for surveying is $11 for a low-income household, $8.5 for a mid-income household, and $9.5 for a high-income household. The survey must include at least 300 households. At least 75 must be high-income homes and at least 145 should be low and mid-income households. The ratio of mid-income to low-income household should not be greater that 3 to 1. Formulate a linear programming model that will minimize surveying costs.

How many decision variables are in this problem?

		None of the amswers given here
		5
		4
		3
		0
		2

How many constraints are there in this problem (do not include the trivial constraints)

		None of the answers given here
		2
		4
		3
		5
		1

1. How many of the constraints are ≤ constraints?

   		3
   		5
   		2
   		1
   		6 or more
   		0

Which of the following is the correct ratio constraint, given that X1 represents low income and X2 mid income?

		-3X1 + X2 ≤ 0
		X1 – 3X2 ≥ 0
		None of the answers given here
		X1 – 3X2 ≤ 0
		3X1 – X2 ≤ 0

The objective function is

		11X1 + 8.5 X2 + 9.5 X3
		None of the answers given here
		11X1 + 8.5 X2
		X1 + X2 + X3
		X1 + X2
		X1 + X2 + X3 ≤ 300

Which constraint belongs to this model?

		None of the answers given here
		X1 + X3 ≥ 145
		X1 + X2 + X3 ≤ 75
		X3 ≥ 75
		X1 ≤ 145

Answer 1

Let the number of low income house hold be X1, mid income house hold be X2 and high income house hold be X3

Objective function

Min Z = 11X1 + 8.5X2 + 9.5X3

Constraints -

X1 + X2 + X3 >= 300 ... must include at least 300 households --- constraint 1

X3 >= 75 ... atleast 75 high income --- constraint 2

X1 + X2 >= 145 ... atleast 145 should be low and mid income --- constraint 3

X2/X1 <= 3/1 => X2 - 3X1 <= 0 ... ratio of mid to low income --- constraint 4

How many decision variables are in this problem?
3 (X1, X2, X3)

How many constraints are there in this problem (do not include the trivial constraints)
4

How many of the constraints are ≤ constraints?
1 (constraint 4)

Which of the following is the correct ratio constraint, given that X1 represents low income and X2 mid income?
-3X1 + X2 ≤ 0

The objective function is
11X1 + 8.5X2 + 9.5X3

Which constraint belongs to this model?
X3 >= 75