Top Toys is planning a new radio and TV advertising campaign. A radio commerical

Question

Top Toys is planning a new radio and TV advertising campaign. A radio commerical costs $300 and a TV ad costs $2000. A total budget of $20,000 is allocated to the campaign. However, to ensure that each medium will have at least one radio commercial and one TV ad, the most that can be allocated to either medium cannot exceed 80% of the total budget. It is estimated that the first radio commerical will reach 5000 people, with each additional commercial reaching only 2000 more people. For TV, the first ad will reach 4500 people, and each additional ad an additional 3000 people. How should the budgeted amount be allocated between radio and TV?

Explanation / Answer

given that each medium will have at least one radio commercial and one tv ad

so, total reach of people is given by

5000(for first radio) + x * 2000 + 4500 (for first tv ad) + y * 3000

where x is extra radio commercial and y is extra tv ad

for dividing budget amount, we have to maximize ( 5000 + x*2000 + 4500 + y*3000) ....(1)

such that

300*(x+1) <= 80% of 20000 => x<=52.3333 , and

2000*(y+1) <= 80% of 20000 => y<=7, and

300*(x+1) + 2000*(y+1) = 20000

=>3*x + 20*y = 177.....(2)

first let x is maximun i.e x=52 (x can not be 52.3333 because x is no of radio)

then from eq 2 , y=1  

which give max reach = 5000 + 52*2000 + 4500 + 1*3000 = 116,500 ...(a)

now

let y is maximum i.e y=7

then from eq 2, x=12 (x can not be 12.3333 because x is no of radio)

which give max reach = 5000 + 12*2000 + 4500 + 7*3000 = 54,500 ...(b)

since, value of (a) > value of (b) i.e 116,500 > 54,500

therefore value of x= 52 and y=1

so amount of radio = 52*300 + 300 = 15900 i.e 79.5%.... (answer)

amount of tv ad = 1* 2000 + 2000 = 4000 i.e 20% ...(answer)

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