# Linear relationship between cost and volume

### Linear Functions

Variable costs vary in a linear fashion with the production level. The following two charts depict this relationship between variable costs and output volume. The reasons for use of straight-line relationships will be explained later assume that the relationship between total cost and volume is direct. Linear cost functions; Linear revenue and profit functions; break-even; Linear A linear cost function expresses cost as a linear function of the number of items.

The study combined both survey research and longitudinal research design. Both primary and secondary data were used for collection. They were analyzed using regression and correlation techniques. The results revealed that the sales value of a product and the quantity of the product manufactured has a positive effect on profit made on the product, also that there is a significant relationship between the cost of production and profit.

The reorder and economic order quantity were also determined as a base for assessing decision making opportunities. Based on the result, the researcher recommends that manufacturing industries should always adopt cost-volume profit analysis in their decision making. Introduction Cost- volume- profit analysis according to Glautieret al is the systematic examination of the inter-relationship between selling prices, sales and production volume, cost, expenses and profits.

The above definition explains cost-volumeprofit analysis to be a commonly used tool providing management with useful information for decision making. Costvolume-profit analysis will also be employed on making vital and reasonable decision when a firm is faced with managerial problems which have cost volume and profit implications.

Such problems are in the areas of profit planning, product planning, make or buy decision, expansion or contraction product line, utilization of productive capacity in a period of economic boom or depression. More especially cost -volume-profit analysis is used by managers to plan and control more effectively and also to concentrate on the relationship among revenues, cost, volume changes, taxes and profit.

It is also known as break-even analysis. Finally this study is aimed at examining the effect of costvolume-profit analysis on decision making process of some selected manufacturing industries in Nigeria. The major problem encountered by manufacturing industries when cost-volume-profit analysis stands as a basis for decision making is managerial inefficiency and this includes ignorance of this concept ie inability of the management to employ it in their decision making and also not knowing the importance of costvolume- profit analysis.

Manufacturing industries are not relevant in their decision making process. Most manufacturing industries in Nigeria do not determine the extent to which cost-volumeprofit analysis affect their various decisions. Manufacturing industries is faced with the problem of how to make use of the available scare resources in order to achieve the objective of profit maximization.

To what extent is cost- volume-profit analysis considered relevant in the decision making process of manufacturing industries? So it's going to be 2x times h.

**What is a Cost Function (Managerial Accounting Tutorial #6)**

The cost of the material is going to be 6. But we have two of these panels. One panel and two panels.

## Fixed and Variable Costs

So we have to multiply by 2. And so we will get-- so this is right over here, this is the cost of the sides. And so let's see if we can simplify this. And I'll write it all in a neutral color. So this is going to be equal to And then you have 2 times 6 times xh.

So this is going to be plus 12xh. And then this is going to be 2 times 6, which is 12 times 2 is 24xh plus 24xh. So this is going to be equal to 20x squared plus 36xh. So this is going to be my cost. But I'm not ready to optimize it yet. We don't know how to optimize with respect to two variables. We only know how to optimize with respect to one variable, and maybe I'll say let's optimize with respect to x. But if we want to optimize with respect to x, we have to express h as a function of x.

So how can we do that? How can we express h as a function of x?

Well, we know that the volume has to be 10 cubic meters. So we know that x, the width times the length times 2x times the height times h needs to be equal to Or another way of saying that, this tells us that 2x squared h, 2x squared times h needs to be equal to And so if we want h as a function of x, we just divide both sides by 2x squared.

## Linear Relationship

And we get h is equal to 10 over 2x squared. Or we could say that h is equal to 5 over x squared. And then we can substitute back right over here. So all of this business is going to be equal to 20 times x squared plus 36 times x times 5 over x squared. So our cost as a function of x is going to be 20x squared 36 times 5. Let's see, 30 times 5 is plus another 30 is going to be So it's going to be plus times, let's see, x times x to the negative 2, x to the negative x to the negative 1 power.

So we finally have cost as a function of x. Now we're ready to optimize. To optimize, we just have to figure out what are the critical points here and whether those critical points are a minimum or a maximum value.

So let's see what we can do. So to find a critical point, we take the derivative, figure out where the derivative is undefined or equal to 0, and those are our candidate critical points.

And then from the critical points we find, they might be minimum or maximum values. So the derivative of c of our cost with respect to x is going to be equal to 40 times x minus times x to the negative 2 power. Now, this seems-- well it's defined for all x except for x equaling 0.

But x equaling 0 is not interesting to us as a critical point because then we're going to have a degenerate. This is going to have no base at all.

### Fixed and Variable Costs - Guide to Understanding Fixed vs Variable

So we don't want to worry about that critical point. We would have no volume at all, so it would not work out. And actually, if x equals 0 then our height is undefined as well. So if I go straight up, where do we intersect our model?

Where do we intersect our line? So it looks like they would get a pretty high score. Let's see, if I were to take it to the vertical axis, it looks like they would get about a So I would write that my estimate is that they would get a 97 based on this model. And once again, this is only a model. It's not a guarantee that if someone studies 3. But you also have to be careful with these models because it might imply if you kept going that if you get, if you study for nine hours, you're gonna get a on the exam, even though something like that is impossible.

So you always have to be careful extrapolating with models, and take it with a grain of salt. This is just a model that's trying to fit to this data. And you might be able to use it to estimate things or to maybe set some form of an expectation, but take it all with a grain of salt.