The demand for your hand-made skateboards, in weekly sales, is
q = −4p + 600
if the selling price is $p. You are prepared to supply
q = 6p − 400
per week at the price $p. What price should you sell your skateboards for so that there is neither a shortage nor a surplus?
well, just set demand = supply and solve for p.
To find the price at which there is neither a shortage nor a surplus, we need to find the price at which the demand is equal to the supply.
First, let's set the demand and supply equations equal to each other:
-4p + 600 = 6p - 400
Now, let's solve for p to find the price:
-4p - 6p = -400 - 600
-10p = -1000
p = -1000 / -10
p = 100
Therefore, the price at which there is neither a shortage nor a surplus is $100.