SOLUTION: I really need some help here getting started...I do not know what I am suppose to do and there are many parts to this but a,b are the key questions I need help with because the oth

Question 465872: I really need some help here getting started...I do not know what I am suppose to do and there are many parts to this but a,b are the key questions I need help with because the other questions work off this.

a. Suppose a market research company finds that at a price of p = $10, they would sell x = 24 tiles each month. If they lower the price to p = $5, then more people would purchase the tile, and they can expect to sell x = 44 tiles in a month�s time. Find the equation of the line for the demand equation. Write your answer in the form p = mx + b. Hint: Write an equation using two points in the form (x,p) and remember that order matters!
b. Substitute the result you found from part a. into the equation R = xp to find the revenue equation. Provide your answer in simplified form.
Found 2 solutions by kingme18, edjones:
Answer by kingme18(98) (Show Source): You can put this solution on YOUR website!
a. Using the hint that was given, you have two points that are (24, 10) and (44, 5) (note that I made sure to put x/number sold, then p/price). To find m (slope), we'll use the slope formula:
=
=
=
Now we just need to find b (y-intercept). One way to do this is to keep in mind that any point on the line will work in the equation, so we can choose either point (I'm going to use 24, 10), plug it into p=mx+b, and solve for b. Remember that we just found out that m=-1/4.

When you write the formula, remember that p and x need to be variables--don't leave (24, 10) in. p=mx+b, but m=-1/4 and b=16, so

b. You were given that R=xp, so we just need to substitute the equation we just found in for p: Then, multiply through by x to simplify:
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
(24,10) & (44,5)
.
(p-p1)/(x-x1)=m
m=(5-10)/(44-24)
=-5/20
=-1/4=-.25 slope
.
(p-p1)=m(x-x1)
p-10=-.25(x-24)
p-10=-.25x+6
p=-.25x+16
.
R=xp
=x(-.25x+16)
=-.25x^2+16x
.
Ed
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