Let's explore some of the limitations and assumptions of cost-volume-profit analysis in our GnG Landscape. We'll return to that same example where managers are evaluating its sod line. And we have information about the average revenue per roll of sod, the average variable cost per roll of sod, and the total fixed costs for the month for this product line. So to think about some of the assumptions that we have identified thus far, the first one was we can categorize costs according to whether they are variable or fixed with some validity. We see that assumption in our first equation, where we have Q = Total FC divided by the SP- VC, or the denominator of contribution margin per unit. We saw substantial changes in the break-even point that we calculated over the series of earlier examples, based on what the level of fixed cost was and based on what the level of variable cost per unit was. But, if at any point in time if we have a mixed cost that we've identified, then we need to estimate what portion of that mixed cost lies in the fixed cost category versus the variable cost category. So the assumption of everything can be categorized is crucial to being able to rely on the output of this equation. It's because what you place in the numerator and what you place in the denominator really determines what the output of this equation will be. To the extent that you've made a mistake or a missed estimation, and called some fixed cost variable, or some variable cost fixed, that's going to influence substantially the validity of the output of this equation. The second assumption underlying cost volume profit analysis that we have identified, is that everything is linear. And then let's call back the example where we had variable cost change from $3 per roll of sod to $4 per roll of sod. Originally, our break-even point was $20,000 was divided by 5- minus the original variable cost and that yielded 10,000 rolls of sod as our break-even point. If we had variable cost change from 3 to 4, our revised Q would have been $20,000 in the numerator divided by 5- the revised variable cost per unit, or 4. And we calculated the break-even point to be 20,000 rolls of sod. This is quite a substantial difference between these two scenarios, all stemming from a very simple $1 change in the variable cost per unit. What we're assuming in terms of everything being linear, is that the other parameters hold under the two different situations that we have calculated. But let's say that in order to produce and sell 20,000 rolls of sod, there's not enough market for that. That we would have to decrease our price of $5 per unit, and offer a discount to those customers to sell that many rolls. That means that if we did not do that and we assume that $20,000 was the break-even point, when we sold $20,000, at the end of the month we would not actually break-even, because we would have changed our selling price. So in a sense, we are assuming that the selling price of $5 per unit is holding, regardless of what level of break-even we are at. And to the extent that that is not true, then the validity of our analysis threatened. And finally, our third assumption had to do with a bit of a cheat I did in devising the equation for the break-even point. At somewhere along the way, we had that 0 = (SP x Q)- (VC x Q)- Total FC. And in one step, we reorganized these terms. We brought Total Fixed Cost to the left hand side of the equation, And then we cheated. We pulled out the Q from both of these terms, we factored out the quantity, and left inside the parenthesis, the contribution margin per unit, or the difference between selling price, and variable cost. Notably, this Q is the same as what we were multiplying the selling price by, as well as what we were multiplying the variable cost by. So in a sense, this Q, if it's the same, both applicable to the selling price and the variable cost. Then this Q is both the number of units that we produce and incur variable cost for, as well as the number of units that we sell and earn a selling price for. So essentially, we're assuming that what we produce in a given period is equivalent to the number of units that we sell. To the extend that we produced more than we sold, than the variable cost driver would be higher than what we used to drive the selling price. And if we sold some units out of our inventory, selling more than what we produced, then the Q that we're multiplying by the selling price would be higher than the Q that we multiplied by the variable cost. So in a sense, this feeds into our third assumption, that the change in inventory over an accounting period is roughly zero. We begin with about same number of units that we end with. And that allows us to identify a Q that applies both to the selling price and the variable cost. Let's have the check point to make sure we understand the implications of these assumptions in our landscape setting.