Class Notes (806,814)
York University (33,494)
Marketing (184)
MKTG 2030 (72)
Ben Kelly (12)
Lecture 3

# Lecture 3.pdf

17 Pages
77 Views

School
York University
Department
Marketing
Course
MKTG 2030
Professor
Ben Kelly
Semester
Winter

Description
OMIS2000 Lecture 3 Jessica Gahtan Lecture 3: Common Business Applications and Excel Solver Common Business Applications Linear  Programming  (LP)  can  be  used  for  many  managerial  decisions :   - Product mix - Media selection - Marketing research - Portfolio selection - Shipping & transportation - Multi-period scheduling For  a  particular  application  we  begin  with  the  problem  scenario  and  data,  then:   1. Define the decision variables 2. Formulate the LP model using the decision variables - Write the objective function equation - Write each of the constraint equations 3. Implement the model in Excel Solver 4. Solve Common  Business  Applications   Product Mix - Usually involve maximizing profit subject to: - Production resource constraints - Material Availability constraints - Standing orders - Quotas - Maximum or minimum proportions Example  1  –  Product  Mix   Imagine that you are managing a factory that is building three products: TV sets, stereos and speakers. Each product is assembled from parts in inventory, and there are five types of parts: Chassis, picture tubes, speaker cones, power supp lies and electronics units. Your goal is to produce the mix of products which will maximize profits, given the inventory of products on hand. Assume that you can sell TV sets for a gross profit of \$75 each, stereos for a profit of \$50 each, and speaker for \$35 each. To assemble a TV set, you need 1 chassis, 1 picture tube, 2 speaker cones, 1 power supply and 2 sets of electronics. To make a stereo, you need 1 chassis, 2 speaker cones, 1 power supply and 1 set of electronics. And to build a speaker, all you need is 1 speaker cone and 1 set of electronics. The parts you have on hand are 450 chassis, 250 picture tubes, 800 speaker cones, 450 power supplies and 600 sets of electronics. You can build only a limited number of products from the parts on hand. a) Formulate the LP model to Maximize the profit. b) Solve using Solver Page 1 of 17 OMIS2000 Lecture 3 Jessica Gahtan Example  1  -­‐  Solution   Step 1: Define the objective - Maximize the profit Step 2: Define the decision variables x1= number of TV sets assembled x2= the number of stereos assembled x3= the number of speakers assembled Step 3: Write the mathematical objective function Maximize Z = 75 x + 50 1 + 35 x 2 3 Step 4: Formulate the constraints 1 x 1 1 x 2 ≤ 450 (Chassis) 1 x ≤ 250 (Picture tubes) 1 2 x 1 2 x +21 x 3 ≤ 800 (Speaker cones) 1 x 1 1 x 2 ≤ 450 (Power supplies) 2 x 1 1 x +21 x 3 ≤ 600 (Electronics) x1, x 2 x 3 ≥ 0 Step 5: Final Formulation Maximize Z = 75 x + 50 1 + 35 x 2 3 S.t: 1 x 1 1 x 2 ≤ 450 (Chassis) 1 x ≤ 250 (Picture tubes) 1 2 x 1 2 x +21 x 3 ≤ 800 (Speaker cones) 1 x 1 1 x 2 ≤ 450 (Power supplies) 2 x 1 1 x +21 x 3 ≤ 600 (Electronics) x1, x 2 x 3 ≥ 0 Some  helpful  notation   xi= # of units of product i produced p=iprofit per unit of product i r = amount of resource j needed to produce one unit of product i ij A j amount of resource j available i= {1,2,3} and j={1,…,5} Solver  Solution   Page 2 of 17 OMIS2000 Lecture 3 Jessica Gahtan Investment Portfolio – Usually involve maximizing return subject to • Maximum risk constraints • Maximum or minimum prop ortions in various asset classes – OR – Minimizing risk subject to • Minimum return constraints • Maximum or minimum proportions in various asset classes Example  2a  –  An  Investment  Example   Welte Mutual Funds, located in New York City, just obtained \$100,000 by co nverting industrial bonds to cash and is now looking for other investment opportunities for these funds. Based on Welte’s current investments, the firm’s top financial analyst recommended that all new investments be made in the oil industry, steel industry or in government bonds. Specifically, the analyst indentified five investment opportunities and projected their annual rates of return. The investments and rates of return are listed below. Management of Welte imposed the following investment guidelines: 1. Neither industry (oil or steel) should receive more than \$50,000 2. Government bonds should be at least 25% of the steel industry investment. 3. The investment in Pacific Oil, the high -return but high risk investment, cannot be more than 60% of the total oil industry investment. What portfolio recommendations - investments and amounts, should be made with the available \$100,000? Example  2a  –  Solution   Step 1: Define the objective • Maximize the return Step 2: Define the decision variables A - Dollars invested in Atlantic Oil P - Dollars invested in Pacific Oil M - Dollars invested in Midwest Steel H - Dollars invested in Huber Steel G - Dollars invested in Government Bonds Step 3: Write the mathematical objective function Maximize Z = 0.073A+ 0.103P+0.064M+0.075H+0.045G Step 4: Formulate the constraints 1. Welte just obtained \$ 100,000 by converting industrial bonds to cash and is now looking for other investment opportunities for these funds. A+P+M+H+G=100,000 2. Neither industry (oil or steel) should receive more than \$50,000 A + P ≤ 50,000 M + H ≤ 50,000 3. Government bonds should be at least 25% of the steel industry investment. 4. The investment in Pacific Oil, the high return but high-risk investment, cannot be more than 60% of the total oil industry investment. Page 3 of 17 OMIS2000 Lecture 3 Jessica Gahtan Step 5: Final Formulation Solver  Solution   Diet Problems – Usually involve minimizing cost of diet subject to • Minimum and maximum nutritional requirements Example  3  –  Diet  Problem   Lifegym, a health and fitness cente r, operates a morning fitness program for senior citizens. The program includes aerobic exercise, either swimming or step exercise, followed by a health breakfast in the dining room. Lifegym’ dietitian wants to develop a breakfast that will be high in calories , calcium, protein and fiber, which are especially important to seniors, but low in fat and cholesterol. She also wants to minimize cost. She has selected the following possible food items, whose individual nutrient contributions and cost from which to develop a standard breakfast menu are shown in the slide. Page 4 of 17 OMIS2000 Lecture 3 Jessica Gahtan Diet Problem – Decision Variables x1= cups of bran cereal x2= cups of dry cereal x3= cups of oatmeal x4= cups of oat bran x5= eggs x6= slices of bacon x7= oranges x8= cups of milk x9= cups of orange juice x = slices of wheat toast 10 Diet Problem – Formulation Formulation - Excel Page 5 of 17 OMIS2000 Lecture 3 Jessica Gahtan Diet Problem – Solution Blending Problems – May be similar to diet problems in that we may minimize the cost of formu lating subject to • Minimum and maximum component requirements – Alternatively we could be maximizing margin or profit earned Example  4a  -­‐  A  Blend  Example   Formulation •
More Less

Related notes for MKTG 2030

OR

Don't have an account?

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Join to view

OR

By registering, I agree to the Terms and Privacy Policies
Just a few more details

So we can recommend you notes for your school.