The easiest method to solve problems like this is to graph the inequalities given and shade the regions that make them true. When you have properly shaded all of the regions, you will find that you have a region which is bounded on all four sides by one of the inequalities, and then you can find the x and y values which correspond to the vertices of the shaded region.
You didn't provide a function that you are trying to maximize in this example, but the idea is that you take all of the (x,y) points which correspond to the vertices and plug them into your objective function. The one which produces the largest value maximizes it (it is a similar process for minimizing it, but you'd be looking for the smallest value). Let me know if you need more help than that, or would like me to work out the example you have provided (I will need an objective function for it though).
It equals 3600 combinations 4(equals the types of cones/cup) x 3(the measures of each one) x 20 (ice cream flavors) x 15 (toppings) += 3600 combinations
