Quiz
IE181
Quiz 1 – Model Formulation
Formulate the following problems. 1. A trade magazine reports the rated exposure (people/month/peso advertising outlay) for each of five media: TV, radio, magazines, newspapers and outdoor advertising as 22, 12, 15, 10 and 5, respectively. The advertising company wants to develop an optimal media mix restricted to the following conditions: a. The total advertising budget is P1 million. b. No more than 50% of the budget is to be expended on radio and TV. c. No more than 30% of the budget is to be expended on any one medium. d. The rated exposure market segmentation targets indicated in the following table must be satisfied: Market Segment | Total Exposure Targets (100,000 people/month) | Rated Exposure by Medium (people/month/peso) | | Min. | Max. | TV | Radio | Magazines | Newspapers | Outdoor Ad | Youth | 25 | 35 | 10 | 5 | 1 | 0 | 1 | Women | 40 | - | 6 | 4 | 7 | 2 | 2 | College Educated | 35 | - | 3 | 1 | 4 | 5 | 1 |
Formulate the LP model that will enable the advertising company to determine how much advertising budget to allocate for each medium/month so as to maximize total monthly exposures.
Answer:
Let x1 = peso expenditures (in P100,000/month) for TV
X2 = peso expenditures (in P100,000/month) for radio x1 = peso expenditures (in P100,000/month) for magazines x1 = peso expenditures (in P100,000/month) for newspapers x1 = peso expenditures (in P100,000/month) for outdoor advertising
Obj. Max Z = 22x1 + 12x2 +15x3 +10x4 +5x5
Subject to: x1 +x2 +x3 +x4 +x5< 10 x1 + x2< 5 x1< 3 x2< 3 x3< 3 x4< 3 x5< 3
10x1 + 5x2 +x3 +x5> 25
10x1 + 5x2 +x3 +x5 <35
6x1 + 4x2 +7x3 +2x4 +2x5> 40
3x1 +2x2 +4x3 +5x4 +x5> 35
Z, xi> 0
2. XYZ Company wants to award contracts for the supply of 4 of its major raw materials. Four (4) suppliers had submitted bids for the materials, with bid prices summarized below: Supplier | Bid
Quiz 1 – Model Formulation
Formulate the following problems. 1. A trade magazine reports the rated exposure (people/month/peso advertising outlay) for each of five media: TV, radio, magazines, newspapers and outdoor advertising as 22, 12, 15, 10 and 5, respectively. The advertising company wants to develop an optimal media mix restricted to the following conditions: a. The total advertising budget is P1 million. b. No more than 50% of the budget is to be expended on radio and TV. c. No more than 30% of the budget is to be expended on any one medium. d. The rated exposure market segmentation targets indicated in the following table must be satisfied: Market Segment | Total Exposure Targets (100,000 people/month) | Rated Exposure by Medium (people/month/peso) | | Min. | Max. | TV | Radio | Magazines | Newspapers | Outdoor Ad | Youth | 25 | 35 | 10 | 5 | 1 | 0 | 1 | Women | 40 | - | 6 | 4 | 7 | 2 | 2 | College Educated | 35 | - | 3 | 1 | 4 | 5 | 1 |
Formulate the LP model that will enable the advertising company to determine how much advertising budget to allocate for each medium/month so as to maximize total monthly exposures.
Answer:
Let x1 = peso expenditures (in P100,000/month) for TV
X2 = peso expenditures (in P100,000/month) for radio x1 = peso expenditures (in P100,000/month) for magazines x1 = peso expenditures (in P100,000/month) for newspapers x1 = peso expenditures (in P100,000/month) for outdoor advertising
Obj. Max Z = 22x1 + 12x2 +15x3 +10x4 +5x5
Subject to: x1 +x2 +x3 +x4 +x5< 10 x1 + x2< 5 x1< 3 x2< 3 x3< 3 x4< 3 x5< 3
10x1 + 5x2 +x3 +x5> 25
10x1 + 5x2 +x3 +x5 <35
6x1 + 4x2 +7x3 +2x4 +2x5> 40
3x1 +2x2 +4x3 +5x4 +x5> 35
Z, xi> 0
2. XYZ Company wants to award contracts for the supply of 4 of its major raw materials. Four (4) suppliers had submitted bids for the materials, with bid prices summarized below: Supplier | Bid