Explain the use of the objective quantity in linear programming.Give an example of an objective quantity that you would minimize and an example of one that you would maximize
In linear programming, the objective quantity is a mathematical expression that represents the goal to be achieved or optimized. It is used to measure the success or efficiency of a solution to a problem. The objective quantity can be either minimized or maximized, depending on the specific problem at hand.
When minimizing an objective quantity, the goal is to find the solution that yields the smallest possible value for that quantity. For example, let's consider a manufacturing company that produces two products: A and B. The company wants to minimize the production cost while meeting certain constraints. The objective quantity to minimize could be the total production cost, which includes factors such as labor, raw materials, and overhead expenses. The company's goal would be to find the production quantities for products A and B that result in the lowest total production cost.
On the other hand, when maximizing an objective quantity, the goal is to find the solution that yields the largest possible value for that quantity. For instance, let's say a company wants to maximize its profits by determining the optimal allocation of advertising budget between different marketing channels. The objective quantity to maximize in this case could be the total revenue generated from each marketing channel. The company's aim would be to allocate the advertising budget in a way that maximizes the overall revenue.
In both cases, linear programming techniques are used to solve the optimization problem and find the optimal solution that minimizes or maximizes the objective quantity.