1. The demand for your hand-made skateboards in weekly sales is q = -3p + 700 if the selling price is $p. You are prepared to supply q = 2p – 500 per week at price $p. At what price should you sell your skateboards so that there is neither shortage nor a surplus?
-3p +700 = 2p -500
+3p +3p
700 = 5p -500
+500 +500
1200 = 5p
/5 /5
$240 = p
To find the price at which there is neither a shortage nor a surplus, we need to set the demand equal to the supply.
The demand equation is q = -3p + 700, where q represents the quantity demanded and p represents the selling price.
The supply equation is q = 2p - 500, where q represents the quantity supplied.
Setting these equations equal to each other, we get:
-3p + 700 = 2p - 500
To solve for p, we need to isolate the p term. We can do this by adding 3p to both sides of the equation:
-3p + 3p + 700 = 2p + 3p - 500
This simplifies to:
700 = 5p - 500
Next, we can add 500 to both sides of the equation:
700 + 500 = 5p - 500 + 500
This simplifies to:
1200 = 5p
Finally, to solve for p, we divide both sides of the equation by 5:
1200/5 = 5p/5
This simplifies to:
240 = p
Therefore, the price at which there is neither a shortage nor a surplus is $240.