help me please, not sure if you can see everything

Question

Answer 1

a)

Find the demand equation :

-85.8x² - 642.199999x + 74698 - 4394 p = 0

4394 p = -85.8x² - 642.199999x + 74698

p = -0.01953x² - 0.1491x + 17

The demand function is quadratic function.

Domain of quadratic function is (-∞, ∞).

Find the supply equation :

88.4x² + 3203.2x + 29016 - 7254 p = 0

7254 p = 88.4x² + 3203.2x + 29016

p = 0.0122x² + 0.4416x + 3.586

The supply function is quadratic function.

Domain of quadratic function is (-∞, ∞).

Answer 2

Demand function.

p = -0.01953x² - 0.1491x + 17               ---------------- (1)

Supply function.

p = 0.0122x² + 0.4416x + 3.586             --------------- (2)

For equilibrium:

-0.01953x² - 0.1491x + 17  = 0.0122x² + 0.4416x + 3.586

0.03173x² + 0.5907x - 13.414 = 0

Solve the quadratic equation.

x = 13.262

p = -0.01953(13.262)² - 0.1491(13.262) + 17

p =11.59

Answer 3

c)

Demand function:

p = -0.01953x² - 0.1491x + 17

Find the revenue function:

R(x) =p*x

        =( -0.01953x² - 0.1491x + 17)*x

        =-0.01953x³ - 0.1491x² + 17x.

Answer 4

Revenue at equilibrium:

At equilibrium x = 13.262

R(x) = -0.01953x³ - 0.1491x² + 17x.

         = -0.01953(13.62)³ - 0.1491(13.262)² + 17(13.262).

         = 150