Question

Suppose a certain outlet chain selling appliances has found that for one brand of home theater, the monthly demand is 160 when the price is $700. However, when the price is $600, the monthly demand is 200. Assuming that the demand function for this system is linear, write the equation for the demand function. Use p for price and q for quantity.

Answer 1

Demand function:

P= D(q)where p is the price and q is the quantity in demand.

We know that if the price is 700 the demand is 210 and if the price is 625 the demand is 255.

To solve this problem, we first need to create the demand function

p = D(q)

and then use it to find the revenue function

Explanation:

R(q)

Now, I may have already given you the answer that you need if all you need is the equation p= D(q). But if you actually have to find the demand function, things get a little more complicated.

Since the demand function is linear, we know that it can be written in slope-intercept form as

p= mx + b

This formula will give you a linear slope showing what happens to q as price goes either up or down. Note that we can write the information you already have in ordered pairs that you can graph: (2.10, 7)(2.55, 6.25). I divided all numbers by 100 to make it easier to graph. You can graph it yourself or go to one of the free online graphing sites