Opening Case-let
Riya was working out certain calculations when Sriman entered her cabin. “What are you doing Riya?” asked Sriman, Market Research Head of Shri Constructions. “I’m working out the number of ads to be placed in these three magazines”, replied Riya, Marketing Manager of the firm.
Looking at the workouts, Sriman said, "If you share the numbers, I can help you". "Yeah Sure!" Riya continued, "Our objective is to achieve a maximum reach of principal buyers through the advertisements in these three leading magazines. I am trying to find the number of advertisements to be placed in each magazine to achieve our objective".
“Do you have the readership details of the magazines and per advertisement costs in those?” asked Sriman. “Yes, …show more content…
Now Riya understood the application of LP model and more confident to solve the issue. “Thanks Sriman for your timely help” acknowledged Riya.
1. What are the elements considered by Sriman to suggest LP formulation for this advertisement problem?
2. Do you think that the linear programming would be really helpful to Riya in decision making? How? 2.2.1 General Mathematical model of Linear Programming Problem
A linear programming problem that has ‘m’ decision variables and ‘k’ constraints is mathematically represented as follows:
LPP is an optimisation technique, the objective function is always ‘to optimize’.
Objective function:
Optimise (Maximise or Minimise) Z = c1.x1 + c2.x2+ … + cm.xm
Subject to constraints such as, a11.x1 + a12.x2 + … + a1m.xm (≤ or ≥ or =) …show more content…
Figure 2.2.1: Linear Programming Problem Formulation
Step 1: Express the objective function, decision variables and constraints in verbal form
Step 2: Ascertain the data that is the values associated with resource constraints, and objective function. These values are not under the control of decision maker but the decision variables are under his control.
Step 3: Express the objective function (Maximise or Minimise) as a linear combination of decision variables and cost or profit coefficients
Step 4: With the help of technology coefficients and resource coefficients, express the constraints as linear equalities or inequalities. If the values of the decision variables satisfy the constraints requirements, then only the LPP solution is said to be feasible.
Step 1 can be skipped, once people gain expertise in LPP formulation. But it should be always kept in mind that a wrong formulation is expensive as it may include an infeasible solution or may exclude an optimal feasible
Riya was working out certain calculations when Sriman entered her cabin. “What are you doing Riya?” asked Sriman, Market Research Head of Shri Constructions. “I’m working out the number of ads to be placed in these three magazines”, replied Riya, Marketing Manager of the firm.
Looking at the workouts, Sriman said, "If you share the numbers, I can help you". "Yeah Sure!" Riya continued, "Our objective is to achieve a maximum reach of principal buyers through the advertisements in these three leading magazines. I am trying to find the number of advertisements to be placed in each magazine to achieve our objective".
“Do you have the readership details of the magazines and per advertisement costs in those?” asked Sriman. “Yes, …show more content…
Now Riya understood the application of LP model and more confident to solve the issue. “Thanks Sriman for your timely help” acknowledged Riya.
1. What are the elements considered by Sriman to suggest LP formulation for this advertisement problem?
2. Do you think that the linear programming would be really helpful to Riya in decision making? How? 2.2.1 General Mathematical model of Linear Programming Problem
A linear programming problem that has ‘m’ decision variables and ‘k’ constraints is mathematically represented as follows:
LPP is an optimisation technique, the objective function is always ‘to optimize’.
Objective function:
Optimise (Maximise or Minimise) Z = c1.x1 + c2.x2+ … + cm.xm
Subject to constraints such as, a11.x1 + a12.x2 + … + a1m.xm (≤ or ≥ or =) …show more content…
Figure 2.2.1: Linear Programming Problem Formulation
Step 1: Express the objective function, decision variables and constraints in verbal form
Step 2: Ascertain the data that is the values associated with resource constraints, and objective function. These values are not under the control of decision maker but the decision variables are under his control.
Step 3: Express the objective function (Maximise or Minimise) as a linear combination of decision variables and cost or profit coefficients
Step 4: With the help of technology coefficients and resource coefficients, express the constraints as linear equalities or inequalities. If the values of the decision variables satisfy the constraints requirements, then only the LPP solution is said to be feasible.
Step 1 can be skipped, once people gain expertise in LPP formulation. But it should be always kept in mind that a wrong formulation is expensive as it may include an infeasible solution or may exclude an optimal feasible