Question

8。The Fashion Store has $12,000 available each month for advertising. Newspaper ads cost $600 apiece and no more than 30 can be run per month. Radio ads cost $300 each and no more than 40 can run per month. TV ads cost $1800 a piece, with a maximum of 6 available each month. Approximately 3000 women will see each newspaper ad, 1800 will hear each radio ad, and 15,000 will see each TV ad. How much of each type of advertising should be used if the store wants to maximize exposure? How many newspaper ads should be placed? How many radio ads should be used? How many TV ads should be run? What is the maximum exposure? women

Answer 1

Let x be number of newspapers should be placed, y be the radio ads and : be TV ads. The equation can be made by, The maximum function is, M 300x +1800y +15000z And constraints are, 600x +300y +1800y s 12000 xs 30 y 340 zs6 The following problem can be solved with the help of MS excel as shown below, Initiate x, y,z 0 and write the formula in constraint as shown below

B5 30 40 1 X JK 0 4 5 Constrain 7 Maximum Also write formula in maximum formula, click on DATA, maximum, by changing variable and add constraint as shown below, Change Constraint Cell Reference: Constraint: SBS1 OK Add Cancel

The final dialog box appears like that, Solver Parameters Set Objective To: By Changing Variable Cellis: SBS7 14im in O Yalue or $B$1:5853 Subject to the Constraints: Add Change Delete BS3SDS3 BS5-SDSS Beset All Load/Save Make Unconstrained Variables Non-Negative Select a Solving Method Simplex LP Options Sohing 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 The red marked shows the ouput as shown below,

E10 30 40 0 2 Y 4 « N 5 Constraint 12000 7Maximum 97200 Therefore, 0 number of newspaper, 4 be the radio ads and 6 be TV ads should be placed to obtain the maximum exposure of 97200.