Sample linear programming problems to calculate max profit, Operation Research

The following linear programming is written to plan the production of two products. And the company wants to maximize profits.

x1 = number of product 1 produced in each batch

x2 = number of product 2 produced in each batch

Max subject to"

150x1+250x2

2x1+ 5x2 <= 200

3x1 + 7x2 <= 175

X1, x2 >= 0

How much profit is earned per each unit of product 2 produced?

a.     150

b.     175

c.      200

d.     250

 Given that

  Max Z = 150 x1 + 250 x2

 Subject to

2x1 + 5x2 <= 200

3x1 + 7x2 <= 175

And x1, x2 >= 0                  

From constraints

  2x1 + 5x2 = 200..............................  (A)

3x1 + 7x2 = 175 ...................................(B)

Or

6x1 + 15x2 = 600

6x1 + 14x2 = 350

Subtracting

X2 = 250

 Put value of x2 in equation (A), we get

2x1 = 200 - 1250 = - 1050

ð X1 = -525 which is meaning less because x1 >= 0, x2>= 0

Thus x1 = 0 and x2 = 250 .

To maximize profit , company should produce 250 units of product 2.

(d) is right answer

10.   Given  that x1 unit of resources 1, and x2 unit of resources 2.

 According to the problem

4x1 + 3x2 <= 150

Thus (b) is right answer 

Posted Date: 7/11/2012 4:33:44 AM | Location : United States







Related Discussions:- Sample linear programming problems to calculate max profit, Assignment Help, Ask Question on Sample linear programming problems to calculate max profit, Get Answer, Expert's Help, Sample linear programming problems to calculate max profit Discussions

Write discussion on Sample linear programming problems to calculate max profit
Your posts are moderated
Related Questions
The sequencing problems arises whenever there is problems in determining the sequence ( order) in which a member of tasks can be performed by a number of service facilities su

Merits a.It is simple  to understand  and easy  to calculate. b.It is very  useful  in the  case of data which  are of  qualitative nature  like  intelligence  honesty  be

Important to Theoretical Distribution The science  of theoretical distribution  under which  the frequencies of a variable are derived by  some  mathematical  model  without

This is determined by disposable personal income( personal income minus direct taxes and other deductions ). Some people suggest the use of discretionary income in place of

difference between simplex solution procedure for maximisation and minimisation

2.Assess the current environmental scan factors that are relevant to the decision making process. Determine the factors that will have the greatest impact on plant operations and m

Maximize p = (3)x + 2y subject to 2x + y 3x + 4y >= 12

How much does cost for developing a simple model using Simuli 8 software and 2 pages write up (Explaining model). This is for my university assignment. For example last year assig

The supply of a certain good is inspected periodically. If an order is placed of size x >0 (integer), the ordering costs are 8+2. x. The delivery time is zero. The demand is stoc

Advantages of Standard  deviation a.Standard  deviation is based on all the observations and is rigidly  defined. b.It is  amenable to algebraic  treatment  and possesses