Sample linear programming problems to calculate max profit, Operation Research

Assignment Help:

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 


Related Discussions:- Sample linear programming problems to calculate max profit

Linear programmibg, A PAPER MILL PRODUCES TWO GRADES OF PAPER VIZ., X AND Y...

A PAPER MILL PRODUCES TWO GRADES OF PAPER VIZ., X AND Y. BECAUSE OF RAW MATERIAL RESTRICTIONS, IT CANNOT PRODUCE MORE THAN 400 TONS OF GRADE X PAPER AND 300 TONS OF GRADE Y PAPER I

Simplex, Maximize Z = 2x - 7y subject -2x + 3y = 3 4x + 5y >= 10 6x + 7y 4...

Maximize Z = 2x - 7y subject -2x + 3y = 3 4x + 5y >= 10 6x + 7y 4x + 8y >= 5

Analytical and decision- making skills, This assessment aims to provide stu...

This assessment aims to provide students with the opportunity to hone their analytical and decision- making skills. It also aims to help students develop their ability to think cre

Sequencing problem, how do you use gantt chart for solving sequencing probl...

how do you use gantt chart for solving sequencing problem ? why is it not employed for solving larger problems?

Table of contents - report writing presentation, Table of contents ...

Table of contents The tables  of contents  is an outline  of the order  of the chapters sections and  sub  section  with their  respective  pages. If  report  includes  a n

Linear programming, nass food produces to kinds of popular dark chocolate b...

nass food produces to kinds of popular dark chocolate bars.the banana and coffee. the banana bar costs 0.22 to make and sells of 0.35, where as the coffee bar costs 0.40 to make an

Rank methods spearman s, Rank Methods Spearman s When the variables  u...

Rank Methods Spearman s When the variables  under  consideration are  not capable  of quantitative  measurement but can  be arranged  in serial  order( ranks) we find  correla

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd