1 The Long Last Appliance Sales Company is in the business of selling appliances

Question

1 The Long Last Appliance Sales Company is in the business of selling appliances such as icrowave ovens, traditional ovens, refrigerators, dishwashers, washers, dryers, and the like. The company has stores in the greater Chicagoland area and has a monthly advertising budget of $90,000. Among its options are radio advertising: advertising in the cable TV channels, newspaper advertising, and direct-mail advertising. A 30-second advertising spot on the local cable channel costs $1,800, a 30-second radio ad costs $350, a half-page ad in the local newspaper costs $700, and a single mailing of direct-mail insertion for the entire region costs $1,200 per mailing. The number of potential buying customers reached per advertising medium usage is as follows Radio 7,000 TV Newspaper Direct mail 50,000 18,000 34,000 Due to company restrictions and availability of media, the maximum number of usages of each medium is limited to the followin Radio TV Newspaper Direct mail 35 25 30 18 The management of the company has met and decided that in order to ensure a balanced utilization of different types of media and to portray a positive image of the company, at least 10 percent of the adv than 40 percent of the advertisements can be on radio. The cost of advertising allocated to TV and direct mail cannot exceed 60 percent of the total advertising budget. Formulate the model which would optimally allocate of the budget among the four media also write down its dual? ertisements must be on TV. No more

Explanation / Answer

Let

Decision Variables:

R = number of radio advertisements

T = number of television spot advertisements

N = number of newspaper advertisements

M = number of direct mail advertisements

Objective Function:

Objective is to maximize the total audience contact by all the means of advertisements.

Max Z = 7,000R + 50,000T + 18,000N + 34,000M

s.t.

Budget Constraint, Budget limit is $90,000

$350R + $1,800R + $700N + $1200M $90,000

Maximum Media Usage:

R 35              Max Radio adtv

T 25              Max TV adtv

N 30                         Max News adtv

M 18                         Max direct mail adtv

Radio advt. must not exceed 50% of the total number of adv.

R 0.5(T + R + N + M)

Or R 0.5T + 0.5R + 0.5N + 0.5M

Or -0.5T + 0.5R - 0.5N - 0.5M 0

TV advt. must account for at least 10% of the total number of adv.

T 0.1(T + R + N + M)

Or T 0.1T + 0.1R + 0.1N + 0.1M

Or 0.9T- 0.1R - 0.1N - 0.1M 0       

Or -0.9T + 0.1R + 0.1N + 0.1M 0 (by changing the inequality sign)

Cost of allocated to TV and direct mail advt. must not exceed 60% of the total advertising budget.

T + M 0.6(90,000)

T + M 54,000

Non-Negativity Constraint:

T, R, N, M 0

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