1 / 11

Linear Programming: System of Inequalities and Profit Maximization

This text introduces linear programming and demonstrates how to solve a system of inequalities and maximize profit using linear programming. It includes examples and step-by-step explanations.

danielharper
Download Presentation

Linear Programming: System of Inequalities and Profit Maximization

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Warm-Up Graph the following system of inequalities. Find the coordinates at each vertices.

  2. Linear Programming 1.6 (M3) p. 30

  3. Vocabulary • Linear programming: maximizing/minimizing a linear objective function. • Objective function: gives quantity that is to maximized or minimized and subject to constraints • Constraints: boundaries of a function • Feasible region: solution area shaded when all constraints are graphed • If bounded (definite shape) then it has a max./min. • The max./min are the vertices.—This is what you substitute into your objective function.

  4. Find the minimum value and the maximum value of the objective function C=3x+2y subject to the following constraints. • Graph the inequalities • Identify the vertices. • Evaluate the function at each vertices looking for the max./min.

  5. Find the minimum value and the maximum value of the objective function C= 4x + 3y subject to the following constraints. Min.: 0, Max.: 32

  6. Find the minimum value and the maximum value of the objective function C= 7x + 5y subject to the following constraints. Min.: 14, Max.: 44

  7. Find the minimum value and the maximum value of the objective function C= 2x + 8y subject to the following constraints. Min.: 0, Max.: 56

  8. Use Linear Programming to maximize profit • Wagons are sold at a craft fair. It takes 4 hours to make a small one and 6 hours to make a large one. The owner will make a profit of $12 for a small wagon and $20 for a large one. He has no more than 60 hours available to make the wagons and wants to have at least 6 small wagons to sell. How many of each size should be made to maximize the profit? • Let x = # of small wagons; y = # of large • Write the equation for profit: • Constraints: • small wagon • Large wagon • Number of hours:

  9. Use Linear Programming to maximize profit Let x = # of small wagons; y = # of large • Write the equation for profit: P = 12x + 20y • Constraints: • small wagon: • Large wagon • Number of hours:

  10. Use Linear Programming to maximize profit Rework the problem if the owner has no more than 40 hours and wants to have at least 4 small wagons to sell.

  11. A storeowner wants to limit the weekly payroll to $960. Employees working regular hours receive $4 per hour, and employees working overtime receive $6 per hour. On the average the store makes $18 for each regular hour of employee work and $32 on each over time hour of employee work. If overtime hours are restricted to at most 2/3 of the regular hours, how should the owner schedule working hours to maximize profit?

More Related