1 / 11

Do the algebra required to find a simultaneous solutions to these two equations (from last class):

Do the algebra required to find a simultaneous solutions to these two equations (from last class): 3x 1 + x 2 = 3 x 1 + 3x 2 = 5. CSC 445/545: Linear Programming. An unofficial course outline and course notes are posted on our class web pages: http://webhome.cs.uvic.ca/~wendym/445.html

iman
Download Presentation

Do the algebra required to find a simultaneous solutions to these two equations (from last class):

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. Do the algebra required to find a simultaneous solutions to these two equations (from last class): • 3x1+ x2=3 • x1 + 3x2=5

  2. CSC 445/545: Linear Programming An unofficial course outline and course notes are posted on our class web pages: http://webhome.cs.uvic.ca/~wendym/445.html Please bring your schedules to class on Mon. to guide me in selection of office hours.

  3. I plan to put Ch. 1 and Ch. 2 on connex in the resources section.

  4. Linear function:given real numbers c0, c1, c2, ..., cn, f(x1, x2, ... , xn) = c0 + c1 x1 + c2 x2+... + cnxn. Linear equation: f(x1, x2, ... , xn) = b. Linear inequalities:f(x1, x2, ... , xn) ≤ b, orf(x1, x2, ... , xn) ≥ b. Linear constraints: linear equations and linear inequalities. Linear programming problem: optimizing (minimizing or maximizing) a linear functions subject to linear constraints.

  5. Standard form (chapters 1-7): Maximize cT x subject to Ax ≤ b and b ≥ 0

  6. The Diet Problem: Find the cheapest diet satisfying certain nutritional requirements using certain foods. m= number of nutrients, n= number of foods, bi , i=1, 2, ..., m = amount of ith nutrient required, cj, j=1, 2, ..., n = cost per unit of jth food, aij = number of units of ith nutrient in jth food, xj, j=1, 2, ..., n = units of jth food in diet. The cost of the diet (objective function): c1 x1 + c2 x2 + c3 x3 + ... + cnxn.

  7. Minimize the cost of the diet: c1 x1 + c2 x2 + c3 x3 + ... + cnxn. To ensure there is an adequate quantity of the ith nutrient, i=1, 2, ..., m (linear constraints): aijxj ≥ bi, i= 1, 2, ...,m To ensure number of units chosen make sense (non-negativity constraints): xj ≥ 0, j=1, 2, ..., n.

  8. We also might have limits on certain foods or beverages. • For example: • Suppose • x2= number of beers • x3= number of glasses of wine • To ensure there are at most 2.5 servings of alcohol in the diet: • x2 + x3 + ≤ 2.5 (also a linear constraint).

  9. Product Mix Problem A manufacturing company produces two models of industrial microwave ovens: X and the Y. Components for both the products need to machined then assembled. It takes 4 hours to machine the components for X and 3 hours to machine the components for Y. A total of 100 machine hours are available per day.

  10. It takes 2 hours to assemble X and 3 hours to assemble Y. There are 48 hours of assembly time available per day. The market potential for X is 15 per day. The market potential for Y is 20 per day. The marketing department wants the company to produce at least 10 products per day, in any combination. Each X contributes $2000 to profit and each Y contributes $2500 to profit. How many X and Y products should be produced per day to maximize profit?

More Related