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Maximum profit.

 Maximum profit. A chain store manager has been told by the main office that daily profit, P, is related to the number of clerks working that day, x, according to the function P = −25x2 + 300x. What number of clerks will maximize the profit, and what is the maximum possible profit? Step by step answers please.
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1 Answer

This is the equation of a parabola that opens downwards (because the coefficient of x2 is negative) so the maximum value of P will be found at the parabola's vertex.
 
The x-coordinate of the vertex is given by:   -b
                                                                 2a
 
Your equation is already in the standard form: (a = -25, b = 300, c = 0) so we can find the x-coordinate at which P will be the maximum.
 
- 300    =   -300     =   6  So six clerks will maximize the profit.
2(-25)        -50
 
To find the maximum profit, plug 6 into the equation for X
 
P = -25 (6)2 + 300(6)
    
   = -25 (36) + 1800
 
   =  -900 + 1800
 
  =  900  this is the maximum profit