Question

At a price of $9 per box of oranges, the supply is 320,000 boxes and at a price of $8.50 per box, the supply is 270,000 boxes. Find the supply equation of the form p = mq + c, where p is the price in dollars and q is the corresponding supply in thousands of boxes.

Answer 1

We want to find a linear equation that models the given situation.

The solution is p = $0.0001*q - $23

The general linear equation is:

p = m*q + c

Where m is the slope and c is the y-intercept.

If we know that the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope can be written as:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Here we have the two points:

price = $9, boxes = 320,000

price = $8.50, boxes = 270,000

We can rewrite these as:

(320,000 , $9)

(270,000 , $8.50)

Then the slope of the line will be:

$m = \frac{\ 9 - \ 8.50}{320,000 - 270,000} = \ 0.00001$

Then the line is something like:

p = $0.0001*q + c

To find the value of c we can use one of the two given points, I will use the first one, (320,000 , $9).

Replacing that in our equation we get:

$9 = $0.0001*320,000 + c  

$9 - $0.0001*320,000  = c = -$23

Then the linear equation is:

p = $0.0001*q - $23

If you want to learn more you can read:

brainly.com/question/11687874