The number of tickets to a rock concert that can be sold is given by the demand

Question

The number of tickets to a rock concert that can be sold is given by the demand model..At a price of p dollars per ticket, the number of tickets that the concert's promoters are willing to make available is given by the supply model.Our demand function is Nd = - 18p + 7100. Our supply function is Ns = 12p + 5900. How many tickets can be sold "

6650

4320

840

290

Does the line y = 9x/4+2 slope up or down ?

Down

" It's non-linear, so sometimes up , other times down "

Up

concave

We want to make sure were remember the natural log function (ln) from highschool math..A model for consumers' response to advertising is given by the equation N(a) = 2600 + 480 ln(a) where N(a) is the number of units sold, a is the amount spent on advertising, in thousands of dollars, and a >= 1. How many units were sold after spending $1,000 on advertising?"

2800

3999

2600

1884

Which of the following explains why knowing the value of X tells you nothing about the value of Y?

The mean of X might be different from the mean of Y.

The variance of X might be different from the mean of Y.

X and Y might be independent.

None of these

6650

4320

840

290

Explanation / Answer

1) How many tickets will be sold will be find by finding equilibrium. The equilibrium is acheived when demand equals supply that gives us equilibrium output and price.

Equate demand and supply function as follows -

- 18p + 7100 = 12p + 5900

12p+18p = 7100-5900

30P = 1200

p = $40

now put p = 40 in either demand or supply function as follows -

Nd = - 18p + 7100 = - 18(40) + 7100 = 6380

6380 is the numbers of tickets that will be sold.

2) Lets first calculate slope of the line as follows-

Let x = 2, thne y = 9x/4 + 2 = 9(2)/4 + 2 = 18/4 + 2 = 6.5.

One coordinate of the line is x=2 and y = 6.5

now lets x = 4, then y = 9(4)/4 + 2 = 9+2 = 11

second coordinate is x=4 and y=11

Now slope = change in y / change in x = (4-2)/(11-6.5) = 2/4.5 = 0.444

As the slope is positive then it goes up that is it si positive.

Hence it is positive.

3) when 1000 is spend on advertising then

a = 1

because a is amount spent on advertising in thousand dollars.

Hence the equation becomes -

N(a) = 2600 + 480In(a)

or

N(a) = 2600 + 480In(1)

we know that In(a) = 0

Thus

N(a) = 2600 + 480(0) = 2600

Thus 2600 units were sold.

4) By getting one variable's value known it is not possible to know the value of other then these two variable are of independent nature. Implying that change in one does not affect other variable.

Thus X and Y might be independent thus  knowing the value of X tells you nothing about the value of Y.

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