Question

The Rapid City Chamber of Commerce periodically sponsors public service seminars and programs which are open to the public. Currently, promotional plans are under way for this year’s program. Advertising alternatives include television, radio, and newspaper. Audience estimates, costs, and maximum media usage limitations are shown below: Television Radio Newspaper Audience per advertisement 70,000 25,000 40,000 Cost per advertisement $1,600 $280 $500 Maximum media usage limitation 19 25 11 Suppose that the production budget is limited to $43,000. We are limited to run at most 43 Ads in all three mediums combined. We need to determine how many commercial messages should be run on each medium so as to reach as many people in Rapid City as possible. Optimal Solution: Number of TV Ads = Number of Radio Ads = Number of Newspaper Ads = Total Audience Reached = Hint: Value should be between 2090800 and 2095200 The Total Cost to buy all of these Ads will be $ DO Not Format your answers …. Leave off Dollar Signs and Commas

Answer 1

Answer:

Number of TV Ads = 19

Number of Radio Ads = 13

Number of Newspaper Ads = 11

Total Audience Reached = 2095000

The Total Cost to buy all of these Ads = 39540

Explanation:

Decision Variables:

A = No. of TV ads

B = No. of Radio ads

C = No. of Newspaper ads

Objective Function:

Max Audience Reach (Z) = 70000*A + 25000*B + 40000*C

Excel LP:

A B C D E F 1 Decision Variable A 0.00 70000 2 B 0.00 25000 G Objective Function Max 0.00 C 0.00 40000 3 Audience per Ad 4 5 Constraints: 6 1600 500 <= 280 0 Total 0 0 0 7 Budget 8 Maximum Usage of TV ads 9 Maximum Usage of Radio ads 10 Maximum Usage of Newspaper ads 11 Maximum total ads 1 0 0 1 0 0 43000 19 25 11 43 1 0 W 1 1 1 0

Formula:

B C D F 1 Decision Variable A B O 10 0 70000 25000 40000 Objective Function =SUMPRODUCT(B2:D2,B3:D3) 2 Max 3 Audience per Ad 4 5 Constraints: 1600 500 <= 280 o 0 6 7 Budget 8 Maximum Usage of TV ads 9 Maximum Usage of Radio ads 10 Maximum Usage of Newspaper ads 11 Maximum total ads Total =SUMPRODUCT($B$2:$D$2,B7:D7) =SUMPRODUCT($B$2:$D$2,B8:D8) =SUMPRODUCT($B$2:$D$2,89:D9 =SUMPRODUCT($B$2:$D$2,B10:010) =SUMPRODUCT($B$2:$D$2,B11:D11) 43000 19 25 11 0 0 0 0 1 1 1 <= 43

solver Parameters:

Solver Parameters X Set Objective: SGS2 1 To: Max Min Value Of: 0 By Changing Variable Cells: $B$2:$D$2 Subject to the Constraints: SB$2:$D$2 >=0 SE$7:SES11 <= SG$7:$G$11 Add Change Delete Reset All Load/Save Make Unconstrained variables Non-Negative 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

Solution:

А B с D E F 1 Decision Variable A 19.00 70000 2 B 13.00 25000 C 11.00 40000 Objective Function |Мах 2095000.00 3 Audience per Ad 4 5 Constraints: 6 Total 39540 1600 <= 280 0 1 7 Budget 8 Maximum Usage of TV ads 9 Maximum Usage of Radio ads 10 Maximum Usage of Newspaper ads 11 Maximum total ads 500 0 0 19 1 0 0 43000 19 25 11 43 13 11 43 1 VV 1 1 1