It might help if you list what the 4 assumptions are. As I understand it, we assume that
1) The objective function is linear in all variables
2) The constraint functions are linear in all variables
3) The coefficients of the linear functions are known and constant
4) The variables are continuous
Let's start by identifying the objective function and the variables. Since this is a business, we presumably want to maximize profit. Our variables are the level of investment in each of three different advertising media, which I'll assume are TV, radio, and internet. Let's call the amount you spend on each of those t, r, and i.
So let's look at assumption 1. Is profit a linear function of investment in those media? Well, probably not. You could consider the case that you buy 1 television commercial during every other break on every channel. If you double your investment and buy 1 commercial during every single break, you're probably going to increase your profit - you've got more visibility for your product. But what happens if you double it again, and buy 2 commercials during every single break. Will your profit continue to increase linearly? Probably not - some potential customers are going to be annoyed that they keep seeing your commercial so often, and they won't buy your cereal. On the other hand, you're likely to get a discount for buying commercials in bulk. So over a large range of the variables, profit probably isn't a linear function. But over a smaller range of variables, and possibly over the range of variables that satisfy the constraints, profit might, in fact, be a linear function.
What about assumption 2, that constraints are linear functions of the variables? Well, for the first constraint you give, that certainly seems to be true - the total dollars you spend, which has to be less than the advertising budget, is simply the sum of the dollars you spend on the three different media:
t + r + i < ad budget
I'm not sure where the planning budget comes into play, so I'm not going to address that.
The number of TV commercials has to be less than some limit. Can we express the number of TV commercials as a linear function of the money spent on TV? Again, maybe not, if you get a discount for buying in bulk. If 1 commercial sells for $1000, and 2 commercials sell for $1800, and 10 commercials sell for $5000, that can't be expressed as a linear function. So it depends on how the commercial rates are structured. You also have to account for commercial rates being different for different shows - a commercial run during the Super Bowl costs much more than a commercial run during the late night programming on the knitting channel. But, depending on the problem, this constraint may never come into play, so you might be able to ignore it, or, again, approximate it as linear over the range of interest.
For the next constraint, you need to reach two target audiences. Can you write a linear function relating the dollars spent on ads to the number of audience members reached? That might be tough, but again, you might be able to make some reasonable linearizing approximations.
I'm not sure how making use of a rebate program would be a constraint to the amount spent on different media. Sorry, I'm just not seeing that relationship.
Ok, third assumption - are the coefficients of all these linear functions (or linear approximations) known and constant? Well, they might not be known right now, but they are presumably knowable, with a little bit of research. Over a relatively short time frame, you'd expect them to be constant, but over longer times, the cost of a TV commercial might change, for example.
Finally, the fourth assumption - are the variables continuous? Well, technically, no. Money is divided into discrete increments - you can't spend a fraction of a cent (assuming you're in the US). But for all practical purposes, if you're talking about spending a large enough sum, those discrete increments approximate a continuum. So you solve the problem as if the variables are continuous, and then round them off to the nearest discrete value, and you don't lose much of the optimality of your solution.
So, the overall question is, can you reasonably use LP to make a decision? If you know the functions and they're reasonably approximated as linear, and you're not planning too far in advance, then yeah. You can at least make a first approximation to the solution, and be somewhat comfortable that you're not missing out on too much potential profit, anyway.
I hope that helps!