A – 1 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Strategic Allocation of Resources (Linear Programming) E For Operations Management, 9e by Krajewski/Ritzman/Malhotra © 2010 Pearson Education Homework: Workshop 1-5.

A – 2 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Overview 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

A – 3 The Maximization Problem BagsTentsResource Availability Cutting2114 Sewing5540 Waterproofing1318 Profit$50$30

A – 4 The Maximization Problem

A – 5 The Maximization Problem

A – 6 The Minimization Problem Grain 1Grain 2Resource Requirement Cutting Sewing Waterproofing Cost$7$2

A – 7 The Minimization Problem

A – 8 The Minimization Problem

A – 9 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.

A – 10 Example LP Formulation: ST capacity barley hops 2:1 ratio minimum P requirement minimum L requirement maximum requirement

A – 11 Example

A – 12 Workshop Problem #1 1. The Ohio Creek Ice Cream Company is planning production for next week. Demand for Ohio Creek premium and light ice cream continue to outpace the company’s production capacities. Ohio Creek earns a profit of $100 per hundred gallons of premium and $100 per hundred gallons of light ice cream. Two resources used in ice cream production are in short supply for next week: the capacity of the mixing machine and the amount of high-grade milk. After accounting for required maintenance time, the mixing machine will be available 140 hours next week. A hundred gallons of premium ice cream requires.3 hours of mixing and a hundred gallons of light ice cream requires.5 hours of mixing. Only 28,000 gallons of high-grade milk will be available for next week. A hundred gallons of premium ice cream requires 90 gallons of milk and a hundred gallons of light ice cream requires 70 gallons of milk.

A – 13 Workshop Problem #2 2. The Sureset Concrete Company produces concrete in a continuous process. Two ingredients in the concrete are sand, which Sureset purchases for $6 per ton, and gravel, which costs $8 per ton. Sand and gravel together must make up exactly 75% of the weight of the concrete. Furthermore, no more than 40% of the concrete can be sand, and at least 30% of the concrete must be gravel. Each day 2,000 tons of concrete are produced.

A – 14 Workshop Problem #3 3. A ship has two cargo holds, one fore and one aft. The fore cargo hold has a weight capacity of 70,000 pounds and a volume capacity of 30,000 cubic feet. The aft hold has a weight capacity of 90,000 pounds and a volume capacity of 40,000 cubic feet. The shipowner has contracted to carry loads of packaged beef and grain. The total weight of the available beef is 85,000 pounds; the total weight of the available grain is 100,000 pounds. The volume per mass of the beef is 0.2 cubic foot per pound, and the volume per mass of the grain is 0.4 cubic foot per pound. The profit for shipping beef is $0.35 per pound, and the profit for shipping grain is $0.12 per pound. The shipowner is free to accept all or part of the available cargo; he wants to know how much meat and grain to accept in order to maximize profit.

A – 15 Workshop Problem #4 4. The White Horse Apple Products Company purchases apples from local growers and makes applesauce and apple juice. It costs $0.60 to produce a jar of applesauce and $0.85 to produce a bottle of apple juice. The company has a policy that at least 30% but not more than 60% of its output must be applesauce. The company wants to meet but not exceed the demand for each product. The marketing manager estimates that the demand for applesauce is a maximum of 5,000 jars, plus an additional 3 jars for each $1 spent on advertising. The maximum demand for apple juice is estimated to be 4,000 bottles, plus an additional 5 bottles for every $1 spent to promote apple juice. The company has $16,000 to spend on producing and advertising applesauce and apple juice. Applesauce sells for $1.45 per jar; apple juice sells for $1.75 per bottle. The company wants to know how many units of each to produce and how much advertising to spend on each in order to maximize profit.

A – 16 Workshop Problem #5 5.MadeRite, a manufacturer of paper stock for copiers and printers, produces cases of finished paper stock at Mills 1, 2, and 3. The paper is shipped to Warehouses A, B, C, and D. The shipping cost per case, the monthly warehouse requirements, and the monthly mill production levels are: Monthly Mill Destination Production A B C D (cases) Mill 1$5.40 $6.20 $4.10 $ ,000 Mill ,000 Mill ,000 Monthly Warehouse Requirement (cases)9,000 9,000 12,000 10,000 How many cases of paper should be shipped per month from each mill to each warehouse to minimize monthly shipping costs?