Question

I have a word problem I’m doing two steps, I’m stuck A vender sells computers, stocks 100 each month80 are sold when priced at $1:000.00 However when priced at $750 all 100 sell Computers are (c) and price is (p) and are linear Write a linear model that relates the number of computers (c) to the price (p)And use the model to estimate how many computers the company would sell if priced at $1425 each

Answer 1

We have a situation where the demand of a computer depends on the price.

We know that quantity sold and price have a linear relationship.

We also know that:

- When priced at $1000 (p = 1000), he sold 80 (q = 80).

- When priced at $750 (p = 750), he sold all the stock (q = 100).

We then have two points for the function: (1000, 80) and (750, 100).

With two points we can define a linear function.

We can calculate the slope of the line as:

$m=\frac{q_2-q_1}{p_2-p_1}=\frac{100-80}{750-1000}=\frac{20}{-250}=-0.08$

Then, we can write the linear function in point-slope form:

$y-80=-0.08(x-1000)$

Now, we can calculate the quantity q for p = 1425:

$\begin{gathered} y-80=-0.08(1425-1000) \\ y=-0.08\cdot425+80 \\ y=-34+80 \\ y=46 \end{gathered}$

Answer:

The linear model is y = -0.08(x-1000) + 80.

For a price of $1425, it is expected that 46 units are sold.