CHAPTER 7
1. Define optimization. Why optimization is important in systems engineering?
Refer in Section 7.1. In the simplest case, optimization is a mathematical
2. , what is
3. , find
4. what is the reflection point for function ? Is this point a
minimum point or maximum point? Why?
To find a reflection point, we need to let
Since
5. Using the unconstrained conditions, find the minimum point for the following function
The Hessian matrix is
6. The cost of a product A is (thousand dollars), with being the number of
the production; the total revenue after selling all the products is (in
thousand dollars), what is the production should be in order to maximize the total profit
(revenue- cost), and what is the maximum profit?
The second order derivatives is
7. Formula the following using LP model
A company is making two types of toy products, product A and product B. Product A makes $50
profit/unit, and product B makes $40 profit/unit. There are four work stations that are needed to
produce A and B, product A uses station 1, 2 and 3 and product B uses station 2, 3,4. The hours
need for two products are listed in the following table as well as the daily production capacity for
each of the station (in hours), make a daily production plan for this company to maximize the
profit.
Station Product A
requirement (hours)
Product B
requirement (hours)
Daily Capacity
(hours)
Define the daily production for A is , daily production for B is , the LP model is
Objective
Subject to
9. A small furniture company is making four different furniture, which uses wood and glasses as
the materials. The production requirements and daily capacity for labor hours and materials are
listed in the following table. Formulate it using LP
Furniture
type
Labor hours
needed
(hr/unit)
Wood (per
unit)
Glasses (per
unit)
Profit
($/unit)
Maximum
allowable
production
(units per
day)
: the daily production of the furniture type
Objective
Subject to
10. Solove the following LP problems graphically
a)
Solution:
c).
11. Solve the above LP problems using Spreadsheet
Here the first question is illustrated, the other two are similar
x1 x2 z
Constraints
x1 x2 Constraints RHS
12. Solve number 8 using Excel.
The excel output is
x1 x2 z