Question

MODULE 1: LP & LP APPLICATIONS (QUESTION 5)

5. DETAILS ASWMSCI 15 4.E.001. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A linear programming computer package is needed. 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 300,000 54,000 120,000 Cost per advertisement $2,000 $300 $600 Maximum media usage 10 20 10 To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. (a) If the promotional budget is limited to $22,800, how many commercial messages should be run on each medium to maximize total audience contact? Television Radio Online What is the allocation of the budget among the three media, and what is the total audience reached? Television Budget Radio Budget Online Budget Total Audience (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

Z max= TV+ Radio+ Online, let TV be X1, Radio X2 and Online X3

Constraints=

• X1+X2+X3> X2/2
• X1>= X1+ X2+ X3/10

A) Promotional budget is 22800, Maximize audience,

Zmax= 300000 * X1 + 54000 * X2 + 120000 * X3

Constraints,

• 2000* X1+ 300*X2+600*X3<= 22800
• X1<=10, X2<=20, X3<=10

Commercial Messages

1. Television- 7
2. Radio- 16
3. Online- 10

Budget

1. Television- 14000
2. Radio- 4800
3. Online- 6000

Total Audience- 41,64,000

B) As we have already maximized the budget, by adding another 100$ , audience won't be increased as it will not have sufficient funds for any of the channel