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TECHNOLOGY IN MATHEMATICS SCIENCES

SMQ3033

Group member Matrix no.

Wahit Bin Siamir D20091035004

Mohd Zulhelmi Bin Hamzah D20091035020

Mohd Faiz Bin Shuib D20091034968

Show & Sell can advertise its products on local radio and television (TV). The Advertising budget is limited to $10000 a month. Each minutes of radio advertising costs $15 and each minute of TV commercial $300. Show & Sell likes to advertise on radio at least twice as much as on TV. In the meantime, it is not practical to use more than 400 minutes of radio advertising a month. From the past experience, advertising on TV is estimated to be 25 times effective as on radio. Determine the optimum allocation of the budget to radio and TV advertising.

The Advertising budget is limited to $10000 a month

Each minutes of radio advertising costs $15 and each minute of TV commercial $300

Advertise on radio at least twice as much as on TV

Not practical to use more than 400 minutes of radio advertising a month

Advertising on TV is estimated to be 25 times effective as on radio

Determine the optimum allocation of the budget to radio and TV advertising?

Combined Constrained Graph

Optimum allocation of the budget to radio and TV advertising located at one of the corner from the shaded reagion

coordinates of extreme point is shown below

A: (60.61, 30.3)

B: (0,0)

C: (400, 0)

D: (400, 13.32)

COORDINATE

X Y Z

A: (60.61, 30.3)

60.61 30.3 818.18

B: (0,0) 0 0 0

C: (400, 0) 400 0 400

D: (400, 13.32)

400 13.32 733

The coordinate that give the highest value of Z is optimum allocation. Thus, the answer is coordinate A

Solution 1: Try And Error

Z = Optimum allocation

Coordinate A: (60.61, 30.3)

Z = X + 25Y

= 60.61 + 25 (30.3)

= 818.18

Using Linear Programming Formula

Optimum time for radio advertising is 60.61 minutes and TV advertising is 30.3 minutes respectively.

Thus, optimum allocation is $818.18

Z = X + 25Y

Optimum allocation = (radio) + 25 (tv)

Optimum allocation = (60.61 minutes) + 25 ( 30.3 minutes)

Optimum allocation = $818.18