Question

Please give one example of REAL LIFE problem that can be formulate as linear programming problem. Make sure you have clear statement about background, the decision variables, objective function and constraints.

Answer 1

Consider, the following real life problem which gives exact ideas about linear programming problem.

A car company produces two models, model A and model B. Long-term projections indicate an expected demand of at least 100 model A cars and 80 model B cars each day. Because of limitations on production capacity, no more than 200 model A cars and 170 model B cars can be made daily. To satisfy a shipping contract, a total of at least 200 cars much be shipped each day. If each model A car sold results in a $2000 loss, but each model B car produces a $5000 profit, how many of each type should be made daily to maximize net profits?

Take a moment to grasp the question.

From the given question, we have:

1. Let a = number of Model A cars per day
2. Let b = number of Model B cars per day

We have the constraints as follows:

a >= 100

b >= 80 

a <= 200

b <= 170

a + b >= 200


P = -2000a + 5000b

And

We want the profit, P to be maximized.

Thank you.