Question 892093
c cost
r revenue
p profit
n how many programs


{{{c=150+0.5n}}}
{{{r=2n}}}
{{{p=r-c}}}
{{{p=2n-(0.5n+150)}}}
{{{highlight(p=2n-n/2-150)}}}


Let {{{p=500}}}
{{{highlight_green(2n-n/2-150=500)}}}
-


{{{(3/2)n-150=500}}}
{{{(3/2)n=650}}}
{{{n=650(2/3)}}}
{{{n=433&1/3}}}

The quantity to sell must be a whole number, so {{{highlight(n>433)}}}.


You could have continued earlier using {{{highlight_green(2n-n/2-150>=500)}}}.