tecnohaa.blogg.se - Graphic lp optimizer

The sum of first-class and coach tickets should be 150 or fewer.

At least 40 coach tickets means that 40 or more should be sold.

At least 25 first-class tickets means that 25 or more should be sold.

No more than 150 tickets can be sold (no more than 150 people can fit on the plane).

In this case, we have the following constraints: Y first class tickets are sold, the total profit for these tickets is 200y.Īs large as possible, provided the constraints are met. X coach tickets are sold, the total profit for these tickets is 225x. Since the goal is the maximize profits, our objective is identified. The question often helps us identify the objective function.

Next, we need to identify the objective function. Since there are coach and first-class tickets, we identify those as the unknowns. We are asked to find the number of each ticket that should be sold. The first step is to identify the unknown quantities. How many of each ticket should be sold in order to maximize profits? Solution At most, the plane has a capacity of 150 travelers. The company makes a profit of $225 for each coach ticket and $200 for each first-class ticket. For the airline to be profitable, it must sell a minimum of 25 first-class tickets and a minimum of 40 coach tickets. An objective function, that is, a function whose value we either want to be as large as possible (want to maximize it) or as small as possible (want to minimize it).Īn airline offers coach and first-class tickets.In order to have a linear programming problem, we must have: Due to difficulties with strict inequalities (), we will only focus on\le and\ge. Inequality is denoted with familiar symbols,, \le, and \ge. Solving Linear Programming Problems GraphicallyĪ linear programming problem involves constraints that contain inequalities. While we have only mentioned a few, these are allĬonstraints-things that limit you in your goal to get to your destination in as little time as possible. At the same time, you will be facing more or less traffic on certain stretches of the trip, you will need to stop for gas at least once (unless you are driving a hybrid vehicle), and, if you have kids, you’ll definitely need to stop for a restroom break. Your hope is to get there in as little time as possible, hence aiming to minimize travel time.

Think about this: you are traveling from Chandler, AZ, to San Diego, CA. Instead, our hope is to maximize or minimize some quantity, given a set of constraints. Wouldn’t it be nice if we could simply produce and sell infinitely many units of a product and thus make a never-ending amount of money? In business (and in day-to-day living) we know that we cannot simply choose to do something because it would make sense that it would (unreasonably) accomplish our goal.