Question

This question under Quantitative methods === had no idea under what topics so I put under statistics and Probability
Pls do not handwritten for easy reading === ===
Question:-
1b) Describe a Linear Programming problem in 300 words so that people who have not had any exposure to Microsoft Excel Solver will understand what LP is(Note: Please do not write a textbook-definition-ish description. You have to explain LP in your own words so that someone like your grand-parents or nephew 12 yr old who have not heard about anything about operations research would understand)

Answer 1

Programming refers to plan of action or we can call it as series of action applied to meet particular objective.

The plan of action may to reduce cost of inputs in a firm or to maximise profit of a industry or to win a game with limited player etc.

Programming helps us to achieve optimum benefits from a limited resources to meet the required objective.

Linear means straight or in mathematical words we can say that equations which when plotted in graph gives straight line.The equation used in the programming is linear.

Linear programming deals with the optimisation (ie minimising or maximising) of linear eequation or linear function  subject to some conditions on variables in form of linear equation.

In Linear programming basically we deal with problem associated with trade,industry , commerce and military operations .

Now coming to a question

A toy company manufacturers two types of dolls ; Basic version doll A and Deluxe version doll B .Each doll of type B takes twice as long to produce as one type of A and company can produce maximumof 2000 doll a day if it produces basic version. The supply of plastic is sufficient to produce 1500 dolls a day (both A and B together ).Deluxe version requires a fancy dress of which there are 600 per daily available. If company makes profit of of rupees 3 an rupees 5 per doll respectively on doll A and B. How many each to be produce daily in order to maximise profit.

Soln-:

Let there be x type of doll A and y type of doll B

Total profit = 3x+ 5y

Since each type of doll B takes twice as long as to produce one type of A

Total time taken to produce x type of doll A and y type of doll B is x+2y

But company makes maximum of 2000 dolls a day

x+2y2000

Palatic is available to produce 1500 dolls only

x+y1500

Also fancy dress is available for 6oo dolls per day

y600

Numbersof dolls can't be negative

X0

y0

Hence the LP problem for givenproblem is as follows:

Maximise Z=3x+5y

Subjectto constraints

x+2y2000

x +y 1500

x0

y0