Question

The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown: 

Constraint	Television	Radio	Online
Audience per advertisement	150,000	17,000	35,000
Cost per advertisement	$1,500	$250	$500
Maximum media usage	12	18	11

To ensure a balanced use of advertising media, radio advertisements must not exceed 45% of the total number of advertisements authorized. In addition, television should account for at least 10% of the Television Radio Online $1,500 $250 $500 18 total number of advertisements authorized 

(a) If the promotional budget is limited to $24,000, how many commercial messages should be run on each medium to maximize total audience contact? If your answer is zero enter "0" 

What is the allocation of the budget among the three media?

What is the total audience reached? 

(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.

Answer 1

Answer report

Objective Cell (Max)
	Cell	Name	Original Value	Final Value
	$F$4	Audience	0	2218736.8
Variable Cells
	Cell	Name	Original Value	Final Value	Integer
	$C$3	Television	0	12.00	Contin
	$D$3	Radio	0	2.53	Contin
	$E$3	Online	0	10.74	Contin
Constraints
	Cell	Name	Cell Value	Formula	Status	Slack
	$F$6	Budget	24000	$F$6<=$H$6	Binding	0
	$F$7	Max Radio	-8.842105263	$F$7<=$H$7	Not Binding	8.842105263
	$F$8	Min TV	6.66134E-16	$F$8<=$H$8	Binding	0
	$C$3	Television	12	$C$3<=$C$9	Binding	0
	$D$3	Radio	2.526315789	$D$3<=$D$9	Not Binding	15.47368421
	$E$3	Online	10.73684211	$E$3<=$E$9	Not Binding	0.263157895

(a)

Television - 12 messages
Radio - 2.53 messages
Online - 10.74 messages

Television budget - $18,000
Radio budget - $631.58
Online budget - $5,368.42

Total audience reached = 2218736.8

(b)

Sensitivity report

Variable Cells
			Final	Reduced	Objective	Allowable	Allowable
	Cell	Name	Value	Cost	Coefficient	Increase	Decrease
	$C$3	Television	12	45105.26316	150000	1E+30	45105.26316
	$D$3	Radio	2.526315789	0	17000	500	332000
	$E$3	Online	10.73684211	0	35000	15581.81818	1000
Constraints
			Final	Shadow	Constraint	Allowable	Allowable
	Cell	Name	Value	Price	R.H. Side	Increase	Decrease
	$F$6	Budget	24000	69.89473684	24000	138.8888889	5666.666667
	$F$7	Max Radio	-8.842105263	0	0	1E+30	8.842105263
	$F$8	Min TV	6.66134E-16	526.3157895	0	0.5	10.83870968

Note the shadow price of the budget constraint.

So,

an addition $100 budget will get 69.89 * 100 = 6,989 more audience