It is known that the quantity demanded of a certain make of portable hair dryer is x hundred units/week and the corresponding wholesale price is shown below where p is in dollars.

p = sqrt(225 - 5x)
The supplier will make x hundred units of hair dryers available in the market when the wholesale unit price is what follows (with p in dollars).
p = sqrt(36 + 1.8 x)
Determine the producers' surplus if the wholesale market price is set at $9 per unit.

To determine the producer's surplus, we need to find the area between the supply curve and the wholesale price. The producer's surplus represents the excess of what producers are willing to supply at a given price compared to what they actually receive.

First, we need to find the quantity supplied by the supplier when the wholesale price is $9 per unit. Let's substitute $9 into the supply function:

p = sqrt(36 + 1.8x)
9 = sqrt(36 + 1.8x)

Now, we can solve for x. Square both sides of the equation:

81 = 36 + 1.8x

Subtract 36 from both sides:

45 = 1.8x

Divide both sides by 1.8:

x = 25

So, the supplier will make 2500 units of hair dryers available when the wholesale unit price is $9.

Now, let's calculate the producer's surplus. The producer's surplus is given by the difference between the area under the supply curve and the revenue received by the producers when the wholesale price is $9.

To find the area under the supply curve, we need to integrate the supply function from 0 to 25:

∫(sqrt(36 + 1.8x))dx, with limits of integration from 0 to 25

Alternatively, we can simplify the equation by recognizing that the supply function is a half-circle with a radius of sqrt(36). The area of a half-circle is (1/2) * pi * r^2. So, in this case, the area under the supply curve is:

(1/2) * pi * (sqrt(36))^2 = (1/2) * pi * 36 = 18pi

Now, let's calculate the revenue received by the producers. The revenue is given by the quantity supplied multiplied by the wholesale price:

Revenue = Quantity Supplied * Wholesale Price
Revenue = 2500 * $9 = $22,500

Finally, we can calculate the producer's surplus:

Producer's Surplus = Area Under Supply Curve - Revenue
Producer's Surplus = 18pi - $22,500

Note: Since we don't have the exact value of pi, the answer will be an approximation.