Have no idea what to do for this business math question

Question

Answer 1

Rewrite the both equations interms of revenue/price (p):

 

4p + 15x - 1100 = 0 -----> p = 1/4(-15x + 1100)

 

p-x^2 = 70 ----> p = x^2 + 70

 

Equilibrium quantity is where supply = demand 

 

1/4(-15x + 1100) = x^2 + 70

 

4x^2 + 280 = -15x + 1100

 

4x^2 + 15x - 820 = 0

 

x = 1/8 (-15 - sqrt(13345)), 1/8 (-15+sqrt(13345))115.5205

 

x = -16.3150625, 12.5650625

 

Price can not be negative so -16.3150625 does not make sense. so the equilibrium quanitity = 12.565025

 

So revenue at equilibrium = p = x^2 + 70 = 12.5650625^2 + 70 = 227.881

Comments

So confused on how you got to this step

 

x = 1/8 (-15 - sqrt(13345)), 1/8 (-15+sqrt(13345))115.5205

 

x = -16.3150625, 12.5650625

 

Price can not be negative so -16.3150625 does not make sense. so the equilibrium quanitity = 12.565025

 

So revenue at equilibrium = p = x^2 + 70 = 12.5650625^2 + 70 = 227.881

---

4x^2 + 15x - 820 = 0

Find the roots using quadratic formula: for ax^2 + bx + c = 0,

x = (- b ± sqrt(b^2 - 4ac))/2a

Here a = 4, b = 15 and c = -820.

x = (-15 ± sqrt (15^ - 4 * 4 * (-820))/2 * 4

x = (-15 ± sqrt (13345))/8

So, x = 1/8 (-15 - sqrt (13345) , x = 1/8(-15 + sqrt (13345)