In media planning, the media planner has to decide on the optimal number of insertions to be made in various media vehicles so as to maximize some measure of effectiveness. The parameters such as Reach, Gross Opportunities-To-See,  Average Opportunities-To-See, Cost Per Person Reached etc. have to be evaluated for arriving at the optimal decision. In the past, researchers have developed an optimization model for determining the ideal combination of advertisement insertions that maximizes Reach. The constraints considered consist of upper bounds on the number of insertions in a vehicle and an upper bound on the total number of insertions in all vehicles. The optimal solution was obtained using dynamic programming. In this paper it is shown that the optimal solution can be obtained easily without using dynamic programming. A solution method is developed for the general case when there are lower and upper bounds on the number of insertions in each vehicle and also an upper bound on the total number of insertions. The problem of maximizing Reach when there is a budget constraint is also considered. A simple solution method is developed for some specified values of the budget. For other values of the budget, dynamic programming can be used to obtain an optimal solution.