Quiz next class, Wed, Oct. 15 BRING A SCIENTIFIC CALCULATOR!!
Assignment: Go back to p. 330 #3, 5. You had these for homework last time without the objective function. Now do the objective functions. Also do p. 344 #9, 11, 12, 13. In case you're confused about #9, trust your gut instinct. The publisher has a typo on p. 563. It should say y>= 3000 and x <= 5000. Also, p. 565, #8 should not have the point (30, 20) in the solution.
Chapter 6 test: Wed, Oct. 21.
Drop by if you have any questions.
Major points from last lesson:
- An optimization problem looks for the MAXIMUM or MINIMUM value of a quantity.
1. Define your variables. (There will be 2.)
Are x and y whole numbers? If x and y are reals, watch out - most of the time, there's an extra restriction that x >=0 and y>= 0.
3. Constraints: Look for language that means >=, <=, >, or <. For example, "up to", "maximum available" mean <=. "At least" means >=. "More than" means >.
There are usually 2 or 3 constraints.
4. Objective function:
This function is in terms of our 2 variables. It's what we want to maximize (e.g., if concerned about revenue or profits) or minimize (e.g., if concerned about costs).
e.g., Revenue = $175x + $110y, where we get $175 for every unit of x and $110 for every unit of y.
5. Graph you constraints: We do not graph the objective function!!
Look for the overlapping region, or intersection. In optimization problems, this is called the FEASIBLE REGION. Label the coordinates of each of your CORNER POINTS in the feasible region.
6. Answer the question:
Plug each of your corner points into the objective function. Check which point gives you a MAX or MIN. That point tells you how much of x and y you need to MAXIMIZE or MINIMIZE the objective function.