Word Problem

Question

The profit of an organization is calculated by the function P(x)=x squared - 4000x + 780000, where x is the number of units sold.  If the net profit is 3800000, find the number of item sold.

Answer 1

P(z) = x² -4000x + 780000 = 3800000   Solve for x by completing the square

 

x² -4000X = 3800000 - 780000

 

X² -4000x + (4000/2)² = 3800000 - 780000 + 2000²

 

(x - 2000)² = 7020000

 

x - 2000 = +-2649.52

x = 2000+-2649.52

 

Ignoring the negative solution gives x = 4649.5.  So at least 4650 units were sold