Question

using quadratic equation solve this equation
4200 + 15Y -3Y^2 .
substitute Y into
TR = 4350Y - 13Y^2 and TC= Y^3 - 5.5Y^2 + 150Y + 675,
so TR = TC

Answer 1

-3Y² + 15Y + 4200 = 0

-Y² + 5Y + 1400 = 0

-Y² +40Y- 35Y + 1400 = 0

Y (-Y + 40) + 35(-Y+40) =0

(Y+35)(-Y+40) = 0

Y = 40, -35

As here Y is the quantity it cannot be negative, Y = 40

TR = 4350*40 - 13*(40)² = 153200

TC = (40)³ - 5.5(40)² +150(40) +675 = 61825

Profit = 153200 - 61825 = 91375

For TR = TC

4350Y - 13Y² = Y³- 5.5Y² + 150Y + 675,

Y³ +7.5Y² - 4200 +675 = 0

Y =  61.08064 or Y=   -68.7414 or Y = 0.16076