word problem

Question

for a fund raising activity , a charitable organization produces calenders to sell in the community. The profit, y (in dollars), can be approximated by;

y=-1/40x^2+10x-500 where x is the number of calenders produced.

 

a. find the number of calenders that should be produced to maximize the profit.

 

b. what is the maximum profit?

Answer 1

(a)

 

Note that y-vs.-x is a parabola.  The maximum occurs at the vertex of the parabola, which is at

 

x = -10/[2(-1/40)] = ?

 

(b)

 

Evaluate y at the x computed in part (a).  That will be your maximum.