Question 1188436
The profit is revenue minus cost, so the profit is {{{x(75-0.0005x)-30x-250000=-0.0005x^2-45x-250000}}}.
Since we want this to equal $750,000, we get
{{{-0.0005x^2+45x-250000=750000}}}
{{{-0.0005x^2+45x-1000000=0}}}
Dividing both sides by {{{-0.0005}}}, we get
{{{x^2-90000x+2000000000}}}.
Factoring, we have {{{(x-40000)(x-50000)=0}}}.
Therefore, the solution is to sell either 40,000 or 50,000 units.