Question 242811
Profit = Revenue - Cost, where Revenue is given, and Cost = $20 *(number of calculators)
Profit = x(32-0.2x)- 20x
{{{32x-0.2x^2 -20x >=155.8}}}
{{{-0.2x^2 +12x -155.8>=0}}}


Divide both sides by -0.2:
{{{x^2-60x+ 779<=0}}}


Completing the square gives this:
{{{x^2 -60x+900<=-779+900}}}
{{{(x-30)^2<=121}}}  


NOTE:  The fact that 121 is a perfect square means that this problem COULD have been solved by factoring.  However, factoring a number like 779 is a DIFFICULT thing to do!!!


The endpoints are at:
{{{x-30=0+-11}}}
{{{x=30+-11}}}
{{{x=30+11=41}}}  or {{{x=30-11=19}}}


Profit will be greater than this amount when x is between 19 and 41 units.  Maximum profit will be at in the middle of this interval at x=30 units.


Graphing calculators and quadratic formula are alternate methods of solving this one.  Let me know if you would like to see either of these methods.


Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus