Retail companies must maintain close path of their operations to keep profitableness. Often, the gross revenues informations of each single merchandise is analyzed individually, which can be used to assist put pricing and other gross revenues schemes.

## Application Practice

Answer the undermentioned inquiries. Use Equation Editor to compose mathematical looks and equations. First, salvage this file to your difficult thrust by choosing Save As from the File bill of fare. Click the white infinite below each inquiry to keep proper data format.

In this job, we analyze the net income found for gross revenues of cosmetic tiles. A demand equation ( sometimes called a demand curve ) shows how much money people would pay for a merchandise depending on how much of that merchandise is available on the unfastened market. Often, the demand equation is found through empirical observation ( through experiment, or market research ) .

Suppose a market research company finds that at a monetary value of P = $ 20, they would sell x = 42 tiles each month. If they lower the monetary value to p = $ 10, so more people would buy the tile, and they can anticipate to sell x = 52 tiles in a month ‘s clip. Find the equation of the line for the demand equation. Write your reply in the signifier P = maxwell + B. Hint: Write an equation utilizing two points in the signifier ( x, p ) .

Slope=Rise and Run Form

x= ( 42-52 ) / ( 20-10 )

x= -10/10

x= -1

p – p1 = m ( x-x1 )

p – 52 = -1 ( x-10 )

p – 52= -x+10

p= -x+62

A company ‘s gross is the sum of money that comes in from gross revenues, before concern costs are subtracted. For a individual merchandise, you can happen the gross by multiplying the measure of the merchandise sold, x, by the demand equation, P.

Substitute the consequence you found from portion a. into the equation R = xp to happen the gross equation. Supply your reply in simplified signifier.

R= x ( -x+62 )

R= -xx+x*62

R= -x^2+62x

The costs of making concern for a company can be found by adding fixed costs, such as rent, insurance, and rewards, and variable costs, which are the costs to buy the merchandise you are selling. The part of the company ‘s fixed costs allotted to this merchandise is $ 300, and the provider ‘s cost for a set of tile is $ 6 each. Let ten stand for the figure of tile sets.

If b represents a fixed cost, what value would stand for B? Is that the fixed cost is $ 300

Find the cost equation for the tile. Write your reply in the signifier C = mx + B.

C= 6x + 300

The net income made from the sale of tiles is found by deducting the costs from the gross.

Find the Net income Equation by replacing your equations for R and C in the equation. Simplify the equation.

P= -x^2+62x- ( 6x+300 )

P= -x^2+62x-6x-300

P= -x^2+56x-300

What is the net income made from selling 20 tile sets per month?

Have to stop up in x=20:

-20^2+56*20-300

P=420

What is the net income made from selling 25 tile sets each month?

Have to stop up in x=25:

-25^2+56*25-300

P=475

What is the net income made from selling no tile sets each month? Interpret your reply.

Have to stop up in x=0:

-0^2+56*0-300

P= -300

Use test and mistake to happen the measure of tile sets per month that yields the highest net income.

X=25, P=475

X=26, P=480

X=27, P=483

X=28, P=484

X=29, P=483

X=30, P=480

If they sell 28 in doing the most profit per month.

How much net income would you gain from the figure you found in portion I?

The net income you earn is found in is $ 484 in when you sell 28.

What monetary value would you sell the tile sets at to recognize this net income? Hint: Use the demand equation from portion a.

P= -x+62

P= -28+62

P= $ 34

The interruption even values for a net income theoretical account are the values for which you earn $ 0 in net income. Use the equation you created in inquiry one to work out P = 0, and happen your interruption even values.

P=0:

P= -x^2+56x-300

0= -x^2+56x-300

0= ( x-6 ) ( x-50 )

X=6 and 50

In 2002, Home Depot ‘s gross revenues amounted to $ 58,200,000,000. In 2006, its gross revenues were $ 90,800,000,000.

Write Home Depot ‘s 2002 gross revenues and 2006 gross revenues in scientific notation.

5.82*10^10

9.08*10^10

You can happen the per centum of growing in Home Depot ‘s gross revenues from 2002 to 2006 by following these stairss:

Find the addition in gross revenues from 2002 to 2006.

( 9.08-5.82 ) *10^10=3.26*10^10 gross revenues

Find what per centum that addition is of the 2002 gross revenues.

3.26*10^10/ ( 5.82*10^10 ) =0.56 is = 56 % 2002 gross revenues

What was the per centum growing in Home Depot ‘s gross revenues from 2002 to 2006? Make all your work by utilizing scientific notation.

The Home Depot, Inc. ( 2007, March 29 ) . 2006 Annual Report. Retrieved from hypertext transfer protocol: //www6.homedepot.com/annualreport/index.html

A client wants to do a tepee in his backyard for his kids. He plans to utilize lengths of PVC plumbing pipe for the supports on the tepee, and he wants the tepee to be 12 pess across and 8 pess tall ( see figure ) . How long should the pieces of PVC plumbing pipe be?

a^2+b^2=c^2

( 12/2 ) ^2+8^2=c^2

6^2+8^2=c^2

C=sqrt ( 6^2+8^2 )

C=sqrt ( 100 )

C= 10 pess Long the PVC Pipe

8 pess

12 pess

How long is the PVC pipe?