A supplier of portable hair dryers will make x hundred units of hair dryers available in the market when the unit price is

p = sqrt(324 + 4x)
dollars. Determine the producers' surplus if the market price is set at $22/unit. (Round your answer to two decimal places.)

22^2=(√(324 + 4x)^2

484 = 324 + 4x
484-324 = 4x
160 = 4x
40 = x

40*22-ʃ (√(324 + 4x))dx on [0,40]
880-4/3( x+81)^3/2 on [0,40]

880-4/3(40+81)^3/2
880-4/3(121)^3/2
880 -802.67 = 77.33

To determine the producer's surplus, we need to find the area of the triangle formed by the supply curve and the market price.

The equation for the supply curve is given by:
p = sqrt(324 + 4x)

where p is the unit price in dollars and x is the number of hundred units.

Given that the market price is set at $22/unit, we can substitute the value of p into the equation:
22 = sqrt(324 + 4x)

To solve for x, we need to isolate it by squaring both sides of the equation:
(22^2) = (sqrt(324 + 4x))^2
484 = 324 + 4x

Now, isolate x:
4x = 484 - 324
4x = 160
x = 40

So, when the market price is set at $22/unit, the supplier will make 40 hundred units available in the market.

Next, we need to calculate the producer's surplus. The producer's surplus is the difference between the total amount received by the supplier and the cost of producing the units.

To find the total amount received, we can multiply the market price by the quantity sold:
Total amount received = Market price * Quantity sold
Total amount received = $22/unit * 40 hundred units

To convert hundred units to units, we multiply by 100:
Total amount received = $22/unit * 40 hundred units * 100 units/hundred units
Total amount received = $22/unit * 4,000 units
Total amount received = $88,000

Now, we need to calculate the cost of producing the units. Given the equation for the unit price:
p = sqrt(324 + 4x)

We can substitute the value of x into the equation:
p = sqrt(324 + 4 * 40)
p = sqrt(324 + 160)
p = sqrt(484)
p = 22

Therefore, the cost of producing the units is $22/unit.

Now, we can calculate the producer's surplus:
Producer's surplus = Total amount received - Cost of producing the units
Producer's surplus = $88,000 - $22/unit * 4,000 units
Producer's surplus = $88,000 - $88,000
Producer's surplus = $0

Therefore, the producer's surplus in this scenario is $0.