Linear Programming –Strategic Allocation of Resources Decision Making with Excel Simulation 1

Homework LP Chapter, #2 (omit money constraint) LP Chapter, #4 LP Supp A, LP Supp B 2

Applications Include Strategic Product or Service Mix Planning Financial Portfolios Choosing the Right Mix (ingredients, diet) Transportation Problems Staff Scheduling Routing Optimize an Objective Function ◦ Minimize Costs ◦ Maximize Profits ◦ Constraints 3

The Maximization Problem BagsTentsResource Availability Cutting2114 Sewing5540 Waterproofing1318 Profit$50$30 4

The Maximization Problem 5

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The Minimization Problem Grain 1Grain 2Resource Requirement Carbos Proteins Fructose Cost$7$2 7

The Minimization Problem 8

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Example-Transportation Problem Delorian motors has 2 distribution centers (DCs) for their 3 dealerships. Delorian automobiles are shipped from the centers to the dealerships. The shipping cost per auto, monthly dealership requirements, and distribution center levels are shown below. How many automobiles should be shipped per month from each DC to each dealership to minimize shipping costs and satisfy dealership demand? 10 Dealership ABCCapacity DC1$5.00$6.00$ DC2$2.00$8.00$ Rqmt

Example 11

Example A local brewery produces three types of beer: premium, regular, and light. The brewery has enough vat capacity to produce 27,000 gallons of beer per month. A gallon of premium beer requires 3.6 pounds of barley and 1.2 pounds of hops, a gallon of regular requires 2.9 pounds of barley and.8 pounds of hops, and a gallon of light requires 2.6 pounds of barley and.6 pounds of hops. The brewery is able to acquire only 55,000 pounds of barley and 20,000 pounds of hops next month. The brewery’s largest seller is regular beer, so it wants to produce at least twice as much regular beer as it does light beer. It also wants to have a competitive market mix of beer. Thus, the brewery wishes to produce at least 4000 gallons each of light beer and premium beer, but not more than 12,000 gallons of these two beers combined. The brewery makes a profit of $3.00 per gallon on premium beer, $2.70 per gallon on regular beer, and $2.80 per gallon on light beer. The brewery manager wants to know how much of each type of beer to produce next month in order to maximize profit. 12

Example LP Formulation: ST capacity barley hops 2:1 ratio minimum P requirement minimum L requirement maximum requirement 13

Example 14

LP Supp A 15

LP Supp B 16