Question

MULTI STEP PROBLEM PLEASE ANSWER ALL.

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 middle income household and $9.5 for a high income household. The survey must include at 300 households. At least 75 must be high income homes and at least 145 should be low and middle income households. The ratio of mid income to low income household should not be greater than 3 to 1. Formulate a linear programming model that minimize surveying costs.

1. How many decision varibles are in this problem?

a.4

b.3

c. Answer not given

d.5

e.2

f.0

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

a.5

b.4

c.Answer not given

d. 3

e.1

f.2

3. How many of the contraints are _< constraints?

a.5

b.2

c.6 or more

d. 1

e. 0

f. 3

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

a.X1-3X2 _>0

b.-3X + X2_<0

c. 3X1-X2_<0

d. X1-3X2__<0

e.answr not given

5. The objective function is

a.11X1+8.5 X2+ 9.5X3

b. 11X1 +8.5 X2

c.X1+X2

d. answer not given

e.X1+X2+X3

f. X1+X2+X3 _<300

6. Which constraint belongs to the model ?

a. Answer not given

b.x3_>75

c.X1+X2+X3_<75

d. X1_<145

e. X1+X3_>145

Answer 1

Answer:

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

1) How many decision variables are in this problem?
ans : 3 (X1, X2, X3) ( option b )

2) How many constraints are there in this problem (do not include the trivial constraints)
ans : 4 ( option b )

3) How many of the constraints are ≤ constraints?
ans : 1 (constraint 4) ( option d )

4) Which of the following is the correct ratio constraint, given that X1 represents low income and X2 mid income?
ans : -3X1 + X2 ≤ 0 ( option b )

5) The objective function is
ans : 11X1 + 8.5X2 + 9.5X3 ( option a )

6) Which constraint belongs to this model?
ans : X3 >= 75 ( option b )

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