Data for this month’s advertising problem for a certain company is described in the table below:

Media Type	Number of Customers Reached per time unit of an Advertisement	Cost ($) per time unit of an Advertisement	Maximum Time Available per Month	Exposure Quality Units per time unit of an Advertisement
Daytime TV	1000	1500	15	65
Evening TV	2000	3000	10	90
Daily newspaper	1500	400	25	40
Sunday newspaper magazine	2500	1000	4	60
Radio	300	100	30	20

At most $30,000 can be spent on advertisements this month. There must be at least 10 time units of TV ads. At most $18,000 may be spent on TV ads. At least 50,000 customers must be reached. The objective is to maximize total exposure quality.

The SOLVER formulation and output is shown below.

	DTV	ETV	DN	SN	R
	10	0	25	2	30
	65	90	40	60	20	2370
Available DTV	1					10	<=	15
Available ETV		1				0	<=	10
Available DN			1			25	<=	25
Available SN				1		2	<=	4
Available R					1	30	<=	30
Budget	1500	3000	400	1000	100	30000	<=	30000
TV restriction 1	1	1				10	>=	10
TV restriction 2	1500	3000				15000	<=	18000
Customers reached	1000	2000	1500	2500	300	61500	>=	50000

The optimal value of the objective function is 2370.

Microsoft Excel Sensitivity Report
Variable Cells
			Final	Reduced	Objective	Allowable	Allowable
	Cell	Name	Value	Cost	Coefficient	Increase	Decrease
	$C$8	DTV	10	0	65	25	65
	$D$8	ETV	0	RC	90	65	1E+30
	$E$8	DN	25	0	40	1E+30	16
	$F$8	SN	2	0	60	40	16.66666667
	$G$8	R	30	0	20	1E+30	14
Constraints
			Final	Shadow	Constraint	Allowable	Allowable
	Cell	Name	Value	Price	R.H. Side	Increase	Decrease
	$H$10	Available DTV	10	SP	15	1E+30	AD
	$H$11	Available ETV	0	0	10	1E+30	10
	$H$12	Available DN	25	16	25	5	5
	$H$13	Available SN	2	0	4	1E+30	2
	$H$14	Available R	30	14	30	20	20
	$H$15	Budget	30000	0.06	30000	2000	2000
	$H$16	TV restriction 1	10	-25	10	1.333333333	1.333333333
	$H$17	TV restriction 2	15000	0	18000	1E+30	3000
	$H$18	Customers reached	FA	0	50000	11500	1E+30

Note that each question below is to be considered independently of all others.

• The Company would like to spend at least 20% of the advertisement cost on the radio. Provide the algebraic formulation of this constraint.

Some values in the Sensitivity report were deleted by the Professor. Complete the table below: Write a brief description of each item deleted using LP terminology and record its corresponding value that belongs in the Sensitivity report.

Number	Item	Description	Value
1	RC
2	SP
3	AD
4	FA

• What is the new optimal value of the objective function, and what are the optimal values of the decision variables (describe verbally the results via a managerial statement), if the objective function coefficient for DN were to decrease from 40 to 30? Justify. 

If the right-hand side of the second constraint (Available ETV) were to increase from 10 to 13, what would be the new optimal value of the objective function? Justify.

If the right-hand side of the seventh constraint (TV restriction 1) were decreased from 10 to 9.5, what would be the new optimal value of the objective function? Justify.

Answer rating: 100% (QA)

What is the new optimal value of the objective function and what are the optimal values of the decis... View the full answer