A large clothing manufacturer has a $7 million budget for advertising for the co

Question

A large clothing manufacturer has a $7 million budget for advertising for the coming year. The board of directors has decided that the following rules should be adhered to when allocating the expenditures: There should be four categories for the expenditure: television, radio, magazines and direct mail. $4 million should be spent on television and radio combined. The total spent on radio and magazines should equal the amount spent on television. All the advertising should be spaced
evenly throughout the year, except for direct mail, which should be evenly spaced in the four months June through September. Only $3 million should be spent in the first six months of the year. Decide how much should be spent in each category.

Explanation / Answer

let Amount spend on tv is t on radio is r on magazines is m and on direct mail is d given t+r+m+d = 7million t+r >= 4 million, r+m = t let a such that t+r=4+a m+d = 3-a r+m=(3-a-d)+(4+a-t) =t 2t = 7-d ---> t = (7-d)/2 r = 4+a-(7-d)/2 = a+d/2+0.5 m = t-r = 3-d - a let d=0 for 1st six months t=3.5*3/7 =1.5 million m=(3-a)*3/7 = 1.286-b million r=(a+0.5)*3/7 = 0.214+b milion where b can be any number

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