graphical method - linear programming

Question 1

it is widely used in mathematical modeling technique designed to help managers in planning and decision making relative to resources allocation

Answer 1

linear programming

Question 2

linear programming belongs to the boarder field of _____

Answer 2

mathematical programming

Question 3

define programming

Answer 3

modeling and solving a problem mathematically

Question 4

what are the 4 common properties of the linear programming

Answer 4

1. all problem seek to max. or min. some quantity (quantity aka the objective function)
   - thr is specific quantity that needs to be max. r min. [in a manufacturing problem, objective cld me maximize profits or minimize cost]
2. restrict that limit the degree to which we can pursue our objective are present
   - thr r constraints tht must be satisfied in order to achieve the objective function [resources, capacity time or other limiting factors]
3. there must be alternative course of action from which to choose
   - thr must be multiple possible solution from which to choose the best one. if thr is only one possible soln, then there is no need for liinear programming
4. the objective and constraints in problems must be expressed in terms of linear equations or inequalities
   - this means tht the the variable in the eqn or inequalities are raised to the power of 1 and multiplied by constants

Question 5

what are the basic assumptions of LP

Answer 5

• certainty
• proportionality
• additivity
• divisibility
• nonnegative (all answers are either 0 or positive no.)

Question 6

properties of LP

Answer 6

• one objective function
• one or more constraints
• alternative course of action
• objective function and constraints are linear - proportionality and divisibility
  certainty
  divisibility
  non-negative variables

Question 7

steps in solving linear programming

Answer 7

use variable to represent the unknown in the problem and tabulate
set up problem in terms of series of mathematical constraints and objective function
convert the inequality explicit constraints into eqn and solve for the terminal points (point of intersection of x axis and y axis)
graph each of the constraints eqn and solve for the intersection if necessary
determine feasible region, that is, the region containing all points tht satisfy the explicit constraints simultaneously
find the vertices of the feasible soln region and sub it to the objective function
choose vertex w highest profit in a maximization problem or lower cost in a minimization problem and write a decision

Question 8

Formulating LP problems

Answer 8

2 or more products are produced during using limited resources such as personnel, machines and raw materials
(if have 2 only can use LP graphical and simplex method)
(but if more than 2, cannot use graphical method, only simplex)

profit that the firm seeks to maximize is based on the profit contribution per unit of each product