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Math Help - hello everyone

  1. #1
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    hello everyone

    hi all, am just new to this forum.. and am hope that this forum will help me out in my maths problems.actually a math question brought me here...and i really need to get a solution for that question.. wish everyone will help me out..
    here is the question

    when the selling price of a packet of 20 cigarettes is $2.5, the weekly demand in the UK is 11 million and when the selling price is $4 the weekly demand is 7.15million.

    a) find the demand function stating q, the weekly demand in millions, in terms of p, the selling price in $, assuming that this is a linear relationship.

    b) suppose that the selling price of a packet of cigarettes is made up of two elements, the sellers revenue per packet and the tax paid to the exchequer per packet . you are given that the sellers revenue is fixed at $1.25 per packet although the tax paid to the exchequer per packet can be changed. find an expression for each of the following in terms of p, the selling price in $
    (1) C- the total combined weekly revenue measured in $millions.
    (2) S- the total seller's weekly revenue measured in $millions.
    (3) E- the total exchequer's weekly revenue measure in $millions

    c) (1) suppose now that packets of 20 cigarettes are sold for $4.75 what is the resulting total exchequer's weekly revenue?

    (2) if the tax per packet is increased to $4.50, find the new total exchequer's weekly revenue and comment on the result including a recommendation to the exchequer.

    so i will be very thankful if someone find me the answers. thanks a lot
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  2. #2
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    I have analyzed this last night. I got stalled at the
    "...find an expression for each of the following in terms of p, the selling price in $
    (1) C- the total combined weekly revenue measured in $millions.
    (2) S- the total seller's weekly revenue measured in $millions.
    (3) E- the total exchequer's weekly revenue measure in $millions"


    Why in terms of p only? When p = 1.25 +t? Should it not be in terms of t?
    t = tax component of p.

    Anyway, to start the ball rolling, here's what I started last night.

    a) find the demand function stating q, the weekly demand in millions, in terms of p, theselling price in $, assuming that this is a linear relationship.

    "Assuming... a linear relationship." So the graph is a straight line. Two points determine a straight line.

    "when the selling price of a packet of 20 cigarettes is $2.5, the weekly demand in the UK is 11 million"
    Using (p,q) ordered pair,
    (2.5,11) ---------------------one point

    "and when the selling price is $4 the weekly demand is 7.15million."
    (4,7.15) ------------other point.

    We can get the equation of the line by using the point-slope form. Say, we use the point (2.5,11),
    (q -11) = [(11 -7.15)/(2.5 -4)](p -2.5)
    q -11 = (-2.566667)(p -2.5)
    q = -2.566667p -6.416667 +11 <----wrong. Should be +6.416667
    q = -2.566667p +6.416667 +11
    q = -2.566667p +17.416667 --------the demand function. (corrected)

    -----------------------------

    Let's see if I can go around the confusion re the C,S,E tonight.
    Last edited by ticbol; August 9th 2007 at 11:44 PM.
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  3. #3
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    thank you very much for your help ,, and would u please try for other parts.. thanks again. take care
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  4. #4
    MHF Contributor
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    Okay, to continue, ....

    b) suppose that the selling price of a packet of cigarettes is made up of two elements, the sellers revenue per packet and the tax paid to the exchequer per packet . you are given that the sellers revenue is fixed at $1.25 per packet although the tax paid to the exchequer per packet can be changed. find an expression for each of the following in terms of p, the selling price in $
    (1) C- the total combined weekly revenue measured in $millions.
    (2) S- the total seller's weekly revenue measured in $millions.
    (3) E- the total exchequer's weekly revenue measure in $millions


    So, p = $(1.25 +t), where t = tax component of the price.

    Revenue = demand*price -----**

    demand = q = -2.566667p +17.416667 -----from previous reply.
    price = p

    So,
    C = [-2.566667p +17.416667](p) ----------answer.

    S = [-2.566667p +17.416667](1.25) -------answer.

    E = [-2.566667p +17.416667](p -1.25) ----answer.

    -------------------------------

    c) (1) suppose now that packets of 20 cigarettes are sold for $4.75 what is the resulting total exchequer's weekly revenue?

    E = [-2.566667p +17.416667](p -1.25)
    E = [-2.566667(4.75) +17.416667](4.75 -1.25)
    E = [5.224999](3.50)
    E = 18.287496 million dollars ---------------answer.

    (2) if the tax per packet is increased to $4.50, find the new total exchequer's weekly revenue and comment on the result including a recommendation to the exchequer.

    then, p = 1.25 +4.50 = $5.75
    So,
    E = [-2.566667p +17.416667](p -1.25)
    E = [-2.566667(5.75) +17.416667](5.75 -1.25)
    E = [2.658332](4.50)
    E = 11.962494 million dollars ---------------answer.

    The 11.962494 million dollars is much less than the 18.287496 million dollars when the tax was $3.50 per pack only. The increase of $1.00 in tax resulted in a loss of (18.287496 -11.962494 = ....) 6.325 million dollars. Because the demand after the $1.00 increase in tax was almost half only of the demand when there was no tax inctrease yet.
    (2.658332 / 5.224999) = 0.50877 -----about half.
    Less demand, less revenue.

    Recommendation to the exhequer?
    What the heck, "You are not good at Math, Echequer! You increase the tax so that you can collect more? Huh!! Why not hire one who can show you simple Math?"

    ---------------
    Now that I am sober, I'd recommend to Taxman to:

    a) If I am against smoking (I am!)...go ahead, keep on increasing the tax. Until the smokies are so expensive the demand would come to a thousand packs per week only. Less demand, less production, less smoke.

    b) If I am for smoking, or if I am included in those benefitting from sales of cigarettes like the Taxman and the manufacturers....reduce the tax!

    Say the tax is reduced $1.00 from the original $3.50. So p = 2.50 +1.25 = $3.75 per pack.
    E = [-2.566667(3.75) +17.416667](2.50) = 19.48 million dollars.
    Umm, an increase of about 1.2 million dollars only for the Taxman. But for the manufacturers, a gain of about 3.2 millions dollars. And for the smokers, an increase of about 2.6 million packs per week. More than enough to smoke out the cobwebs inside the lungs and the linings of the throat.
    Last edited by ticbol; August 11th 2007 at 01:05 PM.
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