The costs of doing business for a company can be found by adding fixed costs, such as rent, insurance, and wages, and variable costs, which are the costs to purchase the product you are selling. The portion of the company’s fixed costs allotted to this product is $300, and the supplier’s cost for a set of tile is $6 each. Let x represent the number of tile sets.

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A company’s revenue is the amount of money that comes in from sales, before business costs are subtracted. For a single product, you can find the revenue by multiplying the quantity of the product sold, x, by the demand equation, p. 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

all of that come from this uppose a market research company finds that at a price of p = $20, they would sell x = 42 tiles each month. If they lower the price to p = $10, then more people would purchase the tile, and they can expect to sell x = 52 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).

from appendix c

On the last part, they are giving you two points on a line (42, 20) and (52, 10). So, you can find the slope of the line from there. Then, using one of the points, you can find b.

i got the first part

its the second part

What is the slope of the line you got?

the first part i got p(x) = -x + 62

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.

R = xp. If p = -x + 62, you can re-write as x = 62-p. So R = ?

c. If b represents a fixed cost, what value would represent b?

First do part b based on my note above. We will worry about part c later.

r =-62?

Revenue can't be a constant. It must depend on price and quantity sold. Quantity sold is based on price. So, revenue must be dependent on price. You have two equations: 1) R = xp 2 x = 62-p. So, substituting (2) into (1), you get R = (62-p)p = 62p - p^2.

is it 300?

Depends on what value of p you use. R = 62p - p^2.

hhmmmm

i'm confused

You said: the first part i got p(x) = -x + 62 Right?

yes

So, all it says is that price (p) and number sold (x) are related by that equation. As you would expect. As price goes up, number of units sold goes down. So far, so good.

Yeah?

ok

Now, the next part of the question says what is the equation for Revenue generated. Revenue = number of items sold * price of each item. R = x times p. Ok so far?

ok

Based on your "demand" equation, x can itself be expressed in terms of p. Because p = -x + 62, you can say x = 62 - p. Substituting this formula for x into the equation for R, you get R = (62-p) times p. Or, R = 62p - p^2

i see that

So, part b is done now.

part c is not clear to me. Is b representing fixed cost per unit? I would think. Total fixed cost is already given as 300.

thats true

its a given

Fixed cost per unit = total fixed cost divided by units sold (x). So, b = 300/x = 300 / (62 - p).

i think so

Based on what was provided, I can't do much further.

thanks for trying though

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