relationship between quantity sold x, resulting price p, is given by x = 100 - 2p.

[glassxx]

The relationship between the number of units sold of a certain product, x, and the price obtained, p, is:

x =100-2p
​
A) Find an expression for the total revenue for selling x units of the product.


B) How many units must be sold for the marginal revenue to be 25?

The total cost of producing x units of the product is:

TC(x)=0.5x^2?+10x+100

C) Find an expression for the profit when producing and selling x units of the product.


D) How many units must be produced and sold to obtain maximum profit?


E) What is the maximum profit?

F) Find an expression for the elasticity, Ep of the demand with respect to p.

G) When is Ep < -1?

 

[stapel]

The relationship between the number of units sold of a certain product, x, and the price obtained, p, is:

. . . . .x = 100 - 2p
​
A) Find an expression for the total revenue for selling x units of the product.

To get this in terms only of "x" (which will be helpful later on), solve the above equation for "p" in terms of x. Then you'll have "x" for the number of units and "p = (something in x)" for the per-unit price.

Then, use what you learned back in algebra and what you know from "real life": What is the relationship between the per-item price, the number of items sold, and the total income from the sale of that number of items? For instance, if you sold ten items at $2 each, how much money did you get in? What mathematical operation did you use to find that number? Apply that same operation in this situation.

B) How many units must be sold for the marginal revenue to be 25?

What definition did they give you for "marginal revenue"? How far have you gotten in applying this information?

The total cost of producing x units of the product is: TC(x) = 0.5x² + 10x + 100

I have edited the posted equation. Did I change it correctly?

C) Find an expression for the profit when producing and selling x units of the product.

What is the relationship between income ("revenues"), outgo ("costs"), and profit? Apply that relationship to the information they've given you (and what you derived) regarding income and outgo.

D) How many units must be produced and sold to obtain maximum profit?

Apply the derivative (or just use what you learned back in algebra) to find the vertex of the upside-down parabola.

E) What is the maximum profit?

Use the vertex info, just like you did when you did max/min problems back in algebra.

F) Find an expression for the elasticity, Ep of the demand with respect to p.

G) When is Ep < -1?

What definition did they give you for "elasticity"? How far have you gotten in applying this information?

Please be complete. Thank you!