In logarithms, power comes ahead of base like :

log (base3)2

will be solved like that :

= 2 log 3

Example :  3log(base 3)2-2log(base 3)6-1/2log(base 3)4

= 2×3log3 -6×2log3-4×0.5log3

= 6log3- 12log3 - 2log3

Now use your calculator to solve the answer.

Where problem is question has two products with several constrainsts, the solution is obtained by Linear programming.

Solution is obtained either by graph or by ISO contribution line.

Limiting factor is any factor which limits the activities of the organization. The most common limiting factor is the sales volume because a company can not sell the entire product it manufactures.

Limiting factor analysis help companies to identify bottleneck resources and use best combination of available resources to maximize profit. Limiting factor in an organization or a company might be raw material, labour time, machine time. Limiting factor analysis can be applied where there is only one limiting factor involved. In case where there are more than one limiting factor, we have to use Linear programming or Simplex method.

Linear programming involves mathematical model which is solved using mathematical equations. The common area on the graph paper is called Feasible Region. The simplex method can only be solved using spread sheet software such as Microsoft Excel. In limiting factor analysis we calculate each product contribution (sales less variable cost) and then divide the contribution by per unit of limiting factor. Let’s suppose raw material N is in short supply (that is it is a limiting factor) For example (Data is based on per unit of each product) :

Product A Sales Price : 100$ ; Product B Sales Price : 200$
Variable Costs A : 50$ Product B : Variable Cost 135$
Contribution Per Unit A ………. 50$
Contribution Per Unit B ………. 50$
N used per unit of A 10 Kg
N used per unit of B 20 Kg

Therefore:
Contribution per Kg A ……….50/10 = 5
Contribution per Kg B ………. 65/20 = 3.25

As you can see Product A Contribution per Kg is greater than that of Product B, so every effort should be made to produce as much units of Product A as possible. After producing all units of product if company still has some kg of raw material N, then it should utilize N to produce Product B. In short the Products are ranked according to Contribution per Kg in order to maximize profitability.

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Author is a student of CIMA (Chartered Institute Of Management Accountants) managerial level.He is also CA-Inter from ICAP (Institute of Chartered Accountant Of Pakistan)

These two cost accounting methods only show differences in short term.In long term both methods reports same profit.

In short term :

1.If closing stock figure is high, then absorption costing will report a high figure than marginal costing.

2. If closing stock is reducing, thenmarginal costing will report a high profit figure than that of absorption costing.

A Japanese term for continuous improvement in production design, process and system.The aim is to reduce idle time.This is just against the standard costing system.

Throughput accounting (TA) is an extreme version of variable costing.It treats only direct material as direct cost and treat other traditional variable cost as fixed like labour and variable overheads.

It emphasizes throughput first, stock minimization second and cost control third.

ratio =  (sales - direct material) / (labour + overhead)