group_ch07_1.doc Page 1 of 1  1/14/04 5:18 PM Name: _______________________

 

OK to do on separate paper if you need more room (and attach).

 

7.107 Consider the following linear program.

               

                        Maximize               30X1 + 10X2

                        Subject to:             3X1 + X2 £ 300

                                                      X1 + X2 £ 200

                                                      X1 £ 100

                                                      X2 ³ 50

                                                      X1 - X2 £ 0

                                                      X1, X2 ³ 0

                Use steps to solve (see handout)

                (a)   Solve the problem using the corner point method.  Is there more than one optimal solution?  Explain.

                (b)   Are there any redundant constraints?

 

7.112  Two advertising media are being considered for promotion of a product.  Radio ads cost $400 each, while newspaper ads cost $600 each.  The total budget is $7,200 per week.  The total number of ads should be at least 15, with at least 2 of each type.  Each newspaper ad reaches 6,000 people, while each radio ad reaches 2,000 people.  The company wishes to reach as many people as possible while meeting all the constraints stated.  How many ads of each type should be placed?

               

                Use steps to formulate and solve (see handout)

 

 

 

 

 

 

 

 

7.107 ANSWER:

                (a) Corner points  (50, 50), (75, 75), (83.33, 50)

                      Optimum solutions:  (75, 75) and (53.33, 50).  Both yield profit of $3,000.

                (b) The constraint X1 £ 100 is redundant since 3X1 + X2 £ 300 also means that X1 cannot exceed 100. X1 + X2 £ 200 is also redundant.

 

7.112  ANSWER:

                Let R = number of radio ads placed

                N = number of newspaper ads placed

 

                Maximize     2000R + 6000N

                Subject to:    R + N ³ 15

                                     400R + 600N £ 7200

                                     R ³ 2

                                     N ³ 2

                                     R, N ³ 0

 

                Feasible corner points (R,N): (9,6) (13,2) (15,2)

                Maximum exposure 54,000 with 9 radio and 6 newspaper ads. Cost = 72,000 ( 400R + 600N £ 7200 )