Problem 4-01 (Algorithmic) The Westchester Chamber of Commerce periodically spon

Question

Problem 4-01 (Algorithmic)

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 newspaper. Audience estimates, costs, and maximum media usage limitations are as shown:

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.

If the promotional budget is limited to $35,600, how many commercial messages should be run on each medium to maximize total audience contact? What is the allocation of the budget among the three media? If required, round your answers to the nearest dollar.

What is the total audience reached? Round your answer to the nearest whole number.

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.

Constraint Television Radio Newspaper Audience per advertisement 100000 18000 20000 Cost per advertisement $2000 $300 $600 Maximum media usage 10 25 15

Explanation / Answer

ANSWER:

Let , 'T' be the number of television spot advertisements,

'R' be the number of radio advertisements, and

'N' be the number of newspaper advertisements

Max 100,000T + 18,000R + 40,000N

s.t. 2,000T + 300R + 600N 35,600 Budget

T 10 (Max Television)

R 20 (Max Radio)

N 10 (Max News)

-0.5T + 0.5R - 0.5N 0 (Max 50% Radio)

0.9T - 0.1R - 0.1N 0 (Max 10% Television)

T, R, N, 0

By trail and error method we obtain the values of T,R, and N

If T = 7, R = 17, N = 20, we get

T = 7 * 2000 = $14,000

R = 17 * 300 = $5100

N = 20 * 600 = $12,000

Total = 31,100

Total Audience reached = 100,000 (7) + 18,000 (17) + 40,000 (20) = 1,806,000

b) The dual price for the budget constraint is 50.73 This is achieved by formulating total budget with the total audience 1,806,000/31,100 = 50.73

Thus, a $100 increase in budget should provide an increase in audience coverage of approximately 5,037.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.