Linear Programming

The course of study is Systems Analysis & Operations research. Solve/Answer all questions in the attached “Assignment 4” document. Must show all
work/calculations. **** The attached PowerPoint and Document labeled “Reference for information only” provides an introduction to Goal Programming*****
Topic introduction
Goal programming is form of Linear Programming (LP) that considers multiple goals that are often in conflict with each other. With multiple goals, all goals
usually cannot be realized exactly. For example, the twin goals of an investor who desires investments with maximum return and with minimum risk are
generally incompatible and therefore unachievable. Other examples of multiple conflicting objectives can be found in organizations that want to: (1)
maximize profits and increase wages; (2) upgrade product quality and reduce product cost; (3) pay larger dividends to stockholders and retain earnings for
growth; and (4) reduce credit losses and increase sales. Goal programming does not attempt to maximize or minimize a single objective function as does the
linear programming model. Rather, it seeks to minimize the deviations among the desired goals and the actual results according to the priorities assigned.
The objective function of a goal programming model is expressed in terms of the deviations from the target goals.

QUESTION 1

SGC Investment Services must develop an investment portfolio for a new client. As an initial investment strategy, the new client would like to restrict the portfolio to a mix of two stocks.

Stock Price/Share ($) Est Annual Return (%)
AGA Products 50 6
Key Oil 100 10

The client wants to invest $50,000 and established the following tow investment goals:

Priority Level 1 Goal
Goal 1: Obtain an annual return of at least 9%

Priority Level 2 Goal
Goal 2: Limit investment in Key Oil, the riskier investment, to no more than 60% of the total investment.

a) Formulate a goal programming model for the SGC Investment problem,
b) What is the investment mix?
 
QUESTION 2

Industrial Chemical produces two adhesives used in the manufacturing for airplanes. The two adhesives, which have different bonding strengths, require different amounts of production time: the IC-100 adhesive requires 20 minutes of production time per gallon of finished product, and the IC-200 adhesives requires 30 minutes of production time per gallon. Both products use 1 pound of highly perishable resin for each gallon of the finished product. Inventory currently holds 300 pounds of resin, and more can be obtained if necessary. However, because of the limited shelf life of the material, any amount not used in the next two weeks will be discarded.

The firm has existing orders for 100 gallons of IC-100 and 120 gallons of IC-200. Under normal conditions, the production process operates eight hours per day, five days per week. Management wants to schedule production for the next two weeks to achieve the following goals:

Priority Level 1 Goals
Goal 1: Avoid underutilization of the production process
Goal 2: Avoid overtime more than 20 hours for the two weeks.

Priority Level 2 Goals
Goal 3: Satisfy existing orders for IC-100 adhesive; that is, produce 100 gallons of IC-100
Goal 4: Satisfy existing orders for IC-200 adhesive; that is, produce 120 gallons of IC-200

Priority Level 3 Goals
Goal 5: Use all the resin

Formulate AND solve a goal programming model for Industrial Chemicals.