Illustration of marginal profit, Managerial Accounting

Illustration of Marginal profit

To illustrate the computations, suppose that the marginal profit or XE in our model is changed from 3 to 3 + δ1, where δ represents either positive or negative change. This means that the objective function reads as: Z = (3 + δ1) XE + 2XI.

If we use this information in the starting tableau and carry out the same arithmetic operations used to produce the optimum tableau, the optimum Z equation will appear as:

1015_table1.jpg


This equation is the same as the optimum Z equation before the change δ1 is effected, modified by terms of δ1. The coefficients of δ1 are essentially those in the XE equation of the optimum tableau, which are

Pivot Element

2322_table2.jpg


We choose the XE equation because XE is the variable whose objective coefficient is being changed by δ1.

The change δ1 will not affect the optimality of the problem as long as all the Z equation coefficients of the non-basic variables remain non-negative (maximization) that is:

1/3 - δ1/3 ≥0

4/3 + 2δ1/3 ≥ 0  

First Relationship  shows that δ1 ≥ 1 and the relation second yields δ1 ≥ -2.  Both relations limit δ1 by -2 ≤ δ1 ≤ 1. This means that the coefficient of XE can be as small as 3 + (-2) = 1 or as large as 3 + 1 = 4 without causing any change in the optimal values of the variables. The optimal value of Z, however, will change according to the expression 12 2/3 + 10/3 δ1 where -2 ≤ δ ≤ 1.

The foregoing discussion assumed that the variable whose coefficient is being changed has an equation in the constraints. This is true only if the variable is basic (such as XE and XI above). If it is non-basic, it will not appear in the basic column.

The treatment of non-basic variable is straight forward. Any change in the objective coefficient of a non-basic variable will affect only that coefficient in the optimal tableau. To illustrate this point, consider changing the coefficient of SI (the first slack variable) from 0 to 0 + δ3. If you carry out the arithmetic operations leading to the optimum tableau, the resulting Z equation becomes:

417_table3.jpg

It shows that the only change occurs in the coefficient of SI, where it is decreased by δ3. As a general rule, then, all we have to do in the case of a non-basic variable is to decrease the Z coefficient of the non-basic variable by the amount by which the original coefficient of the variable is increased.

Posted Date: 12/7/2012 7:04:46 AM | Location : United States







Related Discussions:- Illustration of marginal profit, Assignment Help, Ask Question on Illustration of marginal profit, Get Answer, Expert's Help, Illustration of marginal profit Discussions

Write discussion on Illustration of marginal profit
Your posts are moderated
Related Questions
What are the Advantages or uses of break even charts Computation of break even point or presentation of cost volume and profit relationship by way of break even charts has the

Cash management is related along with the management of: Cash outflows and inflows of the firm Cash flows inside the firm Cash balances as financing deficit and inve

What is Sealed bid pricing Another from of competition oriented pricing is the sealed bid pricing. In a large number of projects, industrial marketing and marketing to the gove

How do the different cost classifications can assist the management

Attributes of good information 1) Information is anything that is communicated and is sometimes said to be processed data. It is data processed in such a way as to be of meaning

Coleman, a married taxpayer, is going to establish a manufacturing business. He anticipates that the business will be profitable immediately due to a patent he holds. He predicts t

Calculate Transfer Price - Management Control System? Question: Compute the Transfer Price for Product X and Y and the Standard Cost of Product Z as the intra company pricing r

Shoe Shine is a local retail shoe shop located on the north side of Centerville. Yearly demand for a popular sandal is 500 pairs, and John Dirk, the manager of Shoe Shine, has been

Rate of return or target pricing method Under this method of price determination first of all a rate of return desired by the enterprises on the amount of profit capital inves

State the factors of CVP The three factors of CVP analysis I e cost volume and profit are interconnected and dependent on one another . for example profit depends upon sales se