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  • Pharmaceutical Firm

    maria flor

    Member

    Updated: Oct 25, 2024
    Views: 1.2K
    A pharmaceutical firm wishes to allocate P50000 towards advertising in newspapers and magazines. This intention of the firm is to maximize the exposure of its advertisement. Each page of the leading newspaper cost P500 and each page of a magazine cost P1000. It is guaranteed that each page of the magazine will reach the audience of 250000 while 50000 persons will read each page of the newspaper ad furthermore, it is specified that at least 1 page of the magazine and newspaper will be allocated for the firms ad. find the number of pages of magazine and newspaper ad that will maximize the exposure and still remain within the budget P50000.
    P.S. P= Pesos(currency of Philippines)

    I need solution for this problem.
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Replies

  • ISHAN TOPRE

    Member • Mar 24, 2011

    I am pretty unsure whether I am right or not because I got the answer in only 5 minutes. But I think that the answer is simple.

    Let x be the variable for newspaper and y be the variable for magazine.

    So we need to maximize z
    where z=500x+1000y
    also 500x=50000 hence x=100

    1000y=250000 hence y=250.

    Drawing the graph of closed region we get the end points as (0,0), (100,0), (0,250), (100,250)
    Hence the number of magazines and newspaper pages are 250 and 100 respectively.


    The value of z is maximum for (100,250)
    What say everyone?
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  • maria flor

    Member • Mar 24, 2011

    @ Ishu: Thanks for trying to answer this. I hope it's correct...😀
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  • ISHAN TOPRE

    Member • Mar 24, 2011

    But Maria have you tried it? Does my solution tally with your ideas?
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  • maria flor

    Member • Mar 24, 2011

    ishutopre
    But Maria have you tried it? Does my solution tally with your ideas?
    I never tried it...Never encountered such problem like that....
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  • maria flor

    Member • Mar 24, 2011

    i found something wrong in your answer ishu...
    500X+ 1000Y=5000
    X=no.of pages in magazine and Y=no.of pages in newspaper. P50000 is the budget.
    If we substitute your answer it's not equal to P50000.
    Correct me if I am wrong...
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  • ISHAN TOPRE

    Member • Mar 24, 2011

    Hi Maria we need to maximize the equation z=500x+1000y

    500= amount for each newspaper page, x =variable and 50000=no of people reading newspaper.

    So 500x=50000 similarly 1000y=250000.

    If you substitute the answers given by me then you get the 'number of people' you can reach in the budget of P50000.
    So you should invest for 250 and 100 pages. of newspaper and magazine each.

    May be I am wrong.
    Let us wait for someone to correct us. 😀
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  • maria flor

    Member • Mar 24, 2011

    Can you please clarify????100 pages for newspapers and 250pages for magazine???
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  • maria flor

    Member • Mar 24, 2011

    Here's my solution:
    Let x= no.of pages of newspapers and y=no.of pages of magazine
    Given: P500 cost of newspaper per page
    P1000cost of magazine per page
    P50000 budget for the ad
    250000audience per page of magazine and 50000audience per page of newspaper.
    Solution:
    500x +1000y = 50000------eq.1
    Max.audience= 50000x +250000y----2
    In order to find the maximum value of x we let y=1
    @y=1, x=98
    While in order to find the maximum value of y we let x=1
    @x=1, y=49.5( but we will you use 49 instead of 50 in order to have a page for newspaper)

    If x=98, y=1 subs.to eq2
    Max.audience= 50000(98) +250000(1),
    Max.audience=5,150,000

    If we let y=49, x=2
    Max.audience= 50000(2) +250000(49),
    Max.audience=12,350,000

    Therefore, the number of pages for magazine is 49 pages while in newspaper is 2 pages.

    correct me if I'm wrong😀
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  • ISHAN TOPRE

    Member • Mar 24, 2011

    Yup Maria. I maximized the wrong thing. But you are right.

    If I may suggest, assume y=50 instead of 49. Because in case of maximizing problems we have to take the highest possible number.

    The rest of method is same. Go ahead. I think the solution is correct. 😀
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  • maria flor

    Member • Mar 25, 2011

    But if we assume y=50 there will be no ad for newspaper
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  • ISHAN TOPRE

    Member • Mar 25, 2011

    OK then Maria if it is so(i.e; y=49) then we have got the answer. Cheers!

    (Sorry I didn't saw that we need 'minimum 1 page condition'.)
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  • maria flor

    Member • Mar 25, 2011

    ishutopre
    OK then Maria if it is so(i.e; y=49) then we have got the answer. Cheers!

    (Sorry I didn't saw that we need 'minimum 1 page condition'.)
    I'm not still sure if that was correct. Let's just wait to other CEans...😀
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  • ssrajmouli

    Member • Apr 14, 2011

    I totally agree with Maria Flor. 49 Magazine pages and 2 Newspaper pages will maximize the exposure.
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