I want to give tickets for a draw depending on two variables (amount purchased, times purchased). The combination of these two would give a number of tickets for the draw. For example, two purchases of 300\$ equal 1 ticket, or one purchase of 500 equal one ticket. The aim is to motivate customers to spend a bit more in order to have more tickets for the draw. There´s an infinite amount of tickets to be offered and the only restrictions are that minimum purchased has to be $500 and that customers in total spend less than \$20,000. I´m thinking of this program as quadratic programming problem, therefore:
Let´s call the times a customer purchased something $y$, the amount spent $x$, and the numer of tickets $k$ the qp problem looks something like these:
$xy + y$ = $k$
$subject$ $to$
$y > 500$
$\sum(x_i*y_i$) $\leq$ 20,000
where $i$ is each time a purchase was made.
I´m not sure how to solve the problem or if there´s a better way to approach it.