Revenue

[mathdad]

The price p (in dollars) and the quantity x sold of a certain product obey the demand equation: x = -20p + 500, where
0 is less than p which is less than or equal to 25.

A. Express the revenue R as a function of x.

Note: use R = px

x = -20p + 500

x - 500 = -20p

(x - 500)/(-20) = p

(-x/20) + 25 = p

R = px

R = [(-x/20) - 25]x

R = (-x^2)/20 + 25x

B. What is the revenue if 20 units are sold?

Let x = 20

R = (-(20)^2)/20 + 25(20)

R = -400/20 + 625

R = -20 + 625

R = 605

Is this right?

 

[Deleted member 4993]

The price p (in dollars) and the quantity x sold of a certain product obey the demand equation: x = -20p + 500, where
0 is less than p which is less than or equal to 25.

A. Express the revenue R as a function of x.

Note: use R = px

x = -20p + 500

x - 500 = -20p

(x - 500)/(-20) = p

(-x/20) + 25 = p

R = px

R = [(-x/20) - 25]x

R = (-x^2)/20 + 25x

B. What is the revenue if 20 units are sold?

Let x = 20

R = (-(20)^2)/20 + 25(20)

R = -400/20 + 625

R = -20 + 625

R = 605

Is this right?

B. What is the revenue if 20 units are sold?
Another way:

x = -20p + 500 → 20 = -20p +500 →1 = -p + 25 → p = 25-1 = 24

R = px → R = 24 * 20 = 480 ...........Oops where did it go wrong

Check your work again......

 

[JeffM]

No. The simplest approach is:

[MATH]q = 500 - 20p \text {, and } r = pq.[/MATH]
[MATH]r = p(500 - 20p) = 500p - 20p^2.[/MATH]
[MATH]q = 20 \implies 20 = 500 - 20p \implies 20p = 480 \implies p = 24.[/MATH]
[MATH]\therefore q = 20 \implies r = 24 * 20 = 480.[/MATH]

 

[Steven G]

The price p (in dollars) and the quantity x sold of a certain product obey the demand equation: x = -20p + 500, where
0 is less than p which is less than or equal to 25.

A. Express the revenue R as a function of x.

Note: use R = px

x = -20p + 500

x - 500 = -20p

(x - 500)/(-20) = p

(-x/20) + 25 = p

R = px

R = [(-x/20) - 25]x

R = (-x^2)/20 + 25x

B. What is the revenue if 20 units are sold?

Let x = 20

R = (-(20)^2)/20 + 25(20)

R = -400/20 + 625

R = -20 + 625

R = 605

Is this right?

25*25=625 so 25*20\(\displaystyle \neq\)625. 25*20=500. Be careful!