The Win Big Gambling Club promotes gambling junkets from a large Midwestern city
ID: 353300 • Letter: T
Question
The Win Big Gambling Club promotes gambling junkets from a large Midwestern city to casinos in the Bahamas. The club has budgeted up to $8,000 per week for local advertising. The money is to be allocated among four promotional media: TV spots, newspaper ads, and two types of radio advertisements. Win Big’s goal is to reach the largest possible high-potential audience through the various media. The following table presents the number of potential gamblers reached by making use of an advertisement in each of the four media. It also provides the cost per advertisement placed and the maximum number of ads that can be purchased per week.
Medium Audience Cost Per Ad Maximum Ads
Reached Per AD per Week
Tv spot (1 minute) 5,000 800 12
Daily newspaper (fullpage
ad) 8,500 925 5
Radio spot (30 seconds,
primetime) 2,400 290 25
Radio spot ( 1minute
afternoon) 2,800 380 20
Win Big’s Contractual arrangements require that at least 5 radio spots be placed each week. To
ensure a broad scoped promotional campaign, management also insists that no more than $1,800 be spent on radio advertising every week.
Microsoft Excel 12.0 Answer Report
Target Cell (Max)
Cell Name Original Value Final Value
$F$6 Audience 0 67240.30
Adjustable Cells
Cell Name Original Value Final Value
$B$5 number of units TV spots 0 1.968
$C$5 number of units news paper ads 0 5
$D$5 number of units prime time ads 0 6.206
$E$5 number of units afternoon spots 0 0
Constraints
Cell Name Cell Value Formula Status Slack
$F$14 min radio spots 6.207 $F$14>=$H$14 Not Binding 1.207
$F$8 max tv 1.969 $F$8<=$H$8 Not Binding 10.031
$F$9 max news paper 5 $F$9<=$H$9 Binding 0
$F$10 max prime time radio 6.207 $F$10<=$H$10 Not Binding ????
$F$11 max afternoon radio 0 $F$11<=$H$11 Not Binding 20
$F$12 budget 8000 $F$12<=$H$12 Binding 0
$F$13 max radio$ 1800 $F$13<=$H$13 Binding 0
Microsoft Excel 12.0 Sensitivity Report
Adjustable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$B$5 number of units Tv spots 1.96875 0 5000 1620.68 5000
$C$5 number of units news paper ads 5 0 8500 1E+30 2718.75
$D$5 number of units prime time ads 6.206896552 0 2400 1E+30 263.157
$E$5 number of units afternoon spots 0 -344.8275862 2800 344.82 1E+30
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$F$14 min radio spots 6.206896552 0 5 1.206 1E+30
$F$8 max tv 1.96875 0 12 1E+30 10.031
$F$9 max news paper 5 2718.75 5 1.702 5
$F$10 max prime time radio 6.206896552 0 25 1E+30 18.79
$F$11 max afternoon radio 0 0 20 1E+30 20
$F$12 budget 8000 6.25 8000 8025 1575
$F$13 max radio$ 1800 2.025 1800 1575 350
Answer the following questions (a-i) using the output please be brief. If there are two possible answers one will suffice. Where necessary a range analysis must be shown.
g) What are the allowable values within which the budget can vary without affecting the
shadow price?- (2 marks)
h) Is the problem degenerate? Explain! (2 marks)
i) Are there alternative optima in this problem? Explain (2 marks)
j) What value should be in the slack column that is given by ???? (1 mark
Explanation / Answer
g) Refer sensitivity report, allowable increase for budget is 8025 and allowable decrease is 1575. Therefore, the allowable values within which the budget can vary without affecting the shadow price are:
Lower limit: 8000-1575 = 6425
Upper limit: 8000+8025 =16025
h) Yes, the problem is degenerate because one of the basic variables (afternoon spots) takes on 0 value.
i) There are no alternative optima in this problem. This is because, there are 7 basic variables (TV (x1), newspaper (x2), primetime (x3), s1, s4, s6, s7) and an equal number i.e. 7 zeros in the objective coefficient (s1,s2,s3,s4,s5,s6,s7)
j) Slack value in Max prime time radio = 25 - 6.207 = 18.793
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