Question

4-01

The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are underway 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	100000	18000	40000
Cost per Advertisement	1400	190	600
Maximum Media Usage	10	10	20

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.

1. If the promotional budget is limited to $20,700, 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.   

Let T = number of television spot advertisements
R = number of radio advertisements
O = number of online advertisements

	Budget ($)
T=
R=
O=
	Total Budget= $

What is the maximum total audience that would be reached? Round your answer to the nearest whole number.

2. 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.

Problem 4-03 (Algorithmic)

The employee credit union at State University is planning the allocation of funds for the coming year. The credit union makes four types of loans to its members. In addition, the credit union invests in risk-free securities to stabilize income. The various revenue-producing investments together with annual rates of return are as follows:

Type of Loan/Investment	Annual Rate of Return (%)
Automobile Loans	8
Furniture Loans	12
Other Secured Loans	14
Signature Loans	13
Risk-Free Securities	9

The credit union will have $2.4 million available for investment during the coming year. State laws and credit union policies impose the following restrictions on the composition of the loans and investments.

• Risk-free securities may not exceed 30% of the total funds available for investment.

• Signature loans may not exceed 10% of the funds invested in all loans (automobile, furniture, other secured, and signature loans).

• Furniture loans plus other secured loans may not exceed automobile loans.

• Other secured loans plus signature loans may not exceed the funds invested in risk-free securities.

How should the $2.4 million be allocated to each of the loan/investment alternatives to maximize total annual return? Round your answers to the nearest dollar.

Automobile Loans
Furniture Loans
Other Secured Loans
Signature Loans
Risk-Free Securities

What is the projected total annual return? Round your answer to the nearest dollar.

Answer 1

Answer
Problem 4-01
1. Calculation of cost per each viewer
Constraint	Television	Radio	Online
Audience per Advertisement	100000	18000	40000
Cost per Advertisement	1400	190	600
Cost per every audience	0.014	0.011	0.015
Media usage times	10	10	20
Net cost per audien	0.014	0.011	0.008
Minimun Budger Required	10%	50%	40%
Minimun Budger Required	2070	10350	8280
No of advertisements (minimum) = Minimum buget divided by cost per ad	1.48	54.47	13.80
No of advertisements (round of)	2	55	12
Cost Final	2800	10450	7200
Note: Since the net cost of online advertisement is less, balance 40% of budget shall be allocated to online. Budget allocated to online is balancing figure.
Total Budget of 20,700 is divided in the given ratio
	No of Ads	Budget	Maximum Audience
T	2	2800	200000
R	55	10450	990000
O	12	7200	480000
Total		20450	1670000
Problem 4-03
Type of Loan/Investment	Annual Rate of Return (%)	Composition (Minimum)	Fund allocated	Constraint	Annual Return
Automobile Loans	8		720000	Note 1.	57600
Furniture Loans	12		360000	Note 1.	43200
Other Secured Loans	14		360000	Fund invested in risk-free securities i.e.e 720000	50400
Signature Loans	13	10%	240000	Maximum 10% of funds	31200
Risk-Free Securities	9	30%	720000	Maximum 30% of funds	64800
			2400000		247200
Note 1: Auto-mobile loan investment shall be equal to Furniture loans and other secured loans.