d(p) = 3200 - 8p
The demand function that the marketing depart is specifying is a simple linear equation. So it will be of the form
d = ap + b
where
d = demand for tablets
p = price of tables
a = slope of demand
b = y intercept
So let's calculate the slope first. We already have one point where price = 350 and demand = 400. We can easily create a second point by subtracting 10 from the price and increasing demand by 80, so the second point is price = 340, demand = 480. Now let's calculate a
a = (480 - 400)/(340 - 350)
a = 80/(-10)
a = -80/10
a = -8/1
a = -8
So our demand function now looks like
d = -8p + b
Let's now solve for b, then plug in the known price and sales figures and calculate. So:
d = -8p + b
d + 8p = b
400 + 8*350 = b
400 + 2800 = b
3200 = b
So our final demand equation is
d = -8p + 3200
Making it a function is
d(p) = 3200 - 8p
