70.2K

Verified Solution

Link Copied!

The optimal value of the objective function is 2370

per Month of an QUESTION 1: LP Formulation and Sensitivity Analysis (24 points) Data for this month's advertising problem for a certain company is described in the table below: Media Type Number of Cost (S) per Maximum Exposure Customers time unit of an Time Quality Units Reached per Advertisement Available per time unit time unit of an Advertisement Advertisement Daytime TV 1000 1500 15 65 Evening TV 2000 3000 10 90 Daily 1500 400 25 40 newspaper Sunday 2500 1000 60 newspaper magazine 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 obiective is to maximize total exposure quality. The SULVEK Iormulation and output is shown below. DTV ETV DN SN R 10 0 25 2 30 4 90 40 60 20 2370 10 10 TV restriction 2 1500 3000 15000 CE 18000 Customers reached 1000 2000 1500 2500 300 81500 50000 Microsoft Excel Sensitivity Report Variable Cells Final Reduced Allowable Objective Coefficient Cell Name Value Cost Allowable Increase 25 Decrease 65 10 0 65 $C$8 SD$8 $E$8 DTV ETV 0 RC 90 65 1E+30 DN 25 0 40 1E+30 16 $F$8 SN 2 0 60 40 16.66666667 SGS8 R 30 0 20 1E+30 14 Constraints Final Shadow Allowable Allowable Constraint R.H. Side Cell Value Price Decrease Increase 1E+30 Name Available DTV Available ETV 10 SP SHS10 SH$11 15 AD 10 0 10 1E+30 SH$12 Available DN 16 25 5 8 No w lola SH$13 Available SN 0 4 1E 30 2 SH$14 14 Available R 30 20 20 SHS 15 30000 006 30000 2000 2000 Budget TV restriction 1 SH$ 16 10 -25 10 1.333333333 1333333333 SH$17 TV restriction 2 15000 0 18000 3000 1E+30 SH$18 Customers reached FA 0 50000 11500 1E430 Note that each question below is to be considered independently of all others. a. The Company would like to spend at least 20% of the advertisement cost on radio. Provide the algebraic formulation of this constraint. (3 points) b. 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. (8 points: 2 points each) NA Tatian Va b. 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. (8 points: 2 points each) Number Item Description Value 1 RC 2 SP 3 AD 4 FA c. 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 302 Justify. (6 points) d. 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. (3 points) e. 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. (4 points) per Month of an QUESTION 1: LP Formulation and Sensitivity Analysis (24 points) Data for this month's advertising problem for a certain company is described in the table below: Media Type Number of Cost (S) per Maximum Exposure Customers time unit of an Time Quality Units Reached per Advertisement Available per time unit time unit of an Advertisement Advertisement Daytime TV 1000 1500 15 65 Evening TV 2000 3000 10 90 Daily 1500 400 25 40 newspaper Sunday 2500 1000 60 newspaper magazine 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 obiective is to maximize total exposure quality. The SULVEK Iormulation and output is shown below. DTV ETV DN SN R 10 0 25 2 30 4 90 40 60 20 2370 10 10 TV restriction 2 1500 3000 15000 CE 18000 Customers reached 1000 2000 1500 2500 300 81500 50000 Microsoft Excel Sensitivity Report Variable Cells Final Reduced Allowable Objective Coefficient Cell Name Value Cost Allowable Increase 25 Decrease 65 10 0 65 $C$8 SD$8 $E$8 DTV ETV 0 RC 90 65 1E+30 DN 25 0 40 1E+30 16 $F$8 SN 2 0 60 40 16.66666667 SGS8 R 30 0 20 1E+30 14 Constraints Final Shadow Allowable Allowable Constraint R.H. Side Cell Value Price Decrease Increase 1E+30 Name Available DTV Available ETV 10 SP SHS10 SH$11 15 AD 10 0 10 1E+30 SH$12 Available DN 16 25 5 8 No w lola SH$13 Available SN 0 4 1E 30 2 SH$14 14 Available R 30 20 20 SHS 15 30000 006 30000 2000 2000 Budget TV restriction 1 SH$ 16 10 -25 10 1.333333333 1333333333 SH$17 TV restriction 2 15000 0 18000 3000 1E+30 SH$18 Customers reached FA 0 50000 11500 1E430 Note that each question below is to be considered independently of all others. a. The Company would like to spend at least 20% of the advertisement cost on radio. Provide the algebraic formulation of this constraint. (3 points) b. 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. (8 points: 2 points each) NA Tatian Va b. 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. (8 points: 2 points each) Number Item Description Value 1 RC 2 SP 3 AD 4 FA c. 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 302 Justify. (6 points) d. 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. (3 points) e. 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. (4 points)

Answer & Explanation Solved by verified expert

See Answer