Question

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sors public service aly pons seminars and programs. Currently, promotional plans are under way for this year's program. Advertising aternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown: Constraint Audience per advertisement 140,00o 18,000 30,000 Cost per advertisement Maximum media usage To ensure a belanced use of advertising media, radio 15% of the total number of advertisements authorized (a) If the promotional budget is limited to $24,100, should be run on Television Radio Online $1,500 $200 550 15 19 12 advertisements must not exceed 45% of the total number of advertisements authorized. In addtion, television how many commercial messages should be run on each medium to maximize total audience contact? If your answer is zero enter "0 No of commercial messages Advertisement Alternatives Television Radio 14 8 Onine 10 What is the ellocation of the budget among the three media? Advertisement Alternatives Budget (s) 8,000 4,200 6,000 Radio Online What is the total audience reached? 1,052,0003 (b) By how much would audience contact increase if an extra $100 were allocated to the promotional budget? Round your answer to the nearest whole number Increase in audience coverage of approximately 5,130

Answer 1

Answer: ---- Date: ----26/04/2019

Max usage! Min% | Max% Audience 140.000 18,000 Cost $1,500 $200 $550 TV Radio Online30,000 15 19 12 15 45 Assume, T as number of television spot advertisements R as number of radio advertisements O as number of online advertisements The constraint for the promotional budget is 1500T + 200R + 5500 x 24,100 R20 T<10 O310 R s0.45(T+R+O) T2 0.15 (T+R+O)

The constraints for the maximum media usage are given as: R320 Ts10 O310 The constraints for the radio advertisement must not exceed 45% of the total number of advertisements as given below: Rs0.45 (T+R+O) The constraints for the television must be at least 15% of the total number of advertisements as given below: T2 0.15 (T+R+O) And, the objective function to maximize the audience is Z- 140,000T 18,000R 30,0000

Hence, the linear programming model is used to maximize the audience as shown below, Z- 140,00T+18,000R+30,0000 Subject to the constraints: 1500T 200R + 5500 3 24,100 RS 20 Ts10 Os 10 R s0.45(T+R+O) T20.1s(T+R*o) And the non-negative constraints are as shown below: TR and o20

Enter the data into a excel sheet as shown below: Audience Cost Min% 15 19 12 Max% Max usauge 1500 200 550 15% 140,000 18,000 30,000 2 TV 3 Radio 4 Online 45% 6 Budget $24,100 Calculate the total audience and cost by using the following formuals are used as showin below: Messages 15 8 0 SUM(B10:B12) 10 TV 11 Radio 12 Online 13 Total 14 15 Spend 16 17 Auidence -SUMPRODUCT(B10:B12,C2:C4) SUMPRODUCT(B10:B12,B2:B4)

Enter all the cell reference and constraints as shown below: Solver Parameters Set Objective: OMn Oyalue of By Changing Variable Cells: 8$10:s8$12 Subject to the Constraints: 8$10-$E$2 $8$13 B$11 <-$F$3 $8$13 Add Change Reset A Load/Save Make Unconstrained Variables Non-Negatve Select a Solving Method: Simplex LP Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth Help Solve Close

Click on slove button the following dialouge box appears Solver Results Solver found a solution. All Constraints and optimality conditions are satisfied. Reports Answer Sensitivity Limits O Keep Solver Solution O Restore Original Values Outline Reports Return to Solver Parameters Dialog Cancel Save Scenario.. OK Solver found a solution. All Constraints and optimality conditions are satisfied. When the GRG engine is used, Solver has found at least a local optimal solution. When Simplex LP is used, this means Solver has found a global optimal solution.

Select on sensitivity report the report will be obtained The final output is obtained as shown below: Audience Cost Max usauge Min% 15 19 12 Max% 1500 200 550 2 TV 3 Radio 4 Online 140,000 18,000 30,000 15% 45% S24,100 6 Budget Message:s 15 8 0 23 10 TV 11 Radio 12 Online 13 Total 14 15 Spend 16 17 Auidence 24100 2244000

The sensitivity report obtained from the solver is as shown below: 6 Variable Cells Reduced Objective Allowable Allowable Final Value Decrease Coefficient Increase 5000 140000 1.00E+30 Cost 15 Name TV Messages Radio Messages Online Messages Cell SB$10 ŞB$11 ŞB$12 8 5000 0 18000 666.666667 7090.91 19500 1.00E+30 10 1950030000 0 12 13 Constraints 14 15 16 17 18 Shadow Constraint Allowable Allowable Final Value R.H. Side Increase 0 Decrease Price Cell SB$10 ŞB$11 ŞB$15 Name TV Messages Radio Messages Spend Messages 11.55 1.00E+30 2.35 1600 0 15 0 1.0OE+30 90 24100 854.545455 24100 According to the above sensitivity report the shadow price for the budget constraints is 90 and the allowable increase is 854. Thus if increase in $100 budget for promotion then it will increase in audience coverage