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M ASSACHUSETTS I NSTITUTE OF T ECHNOLOGY 15.053 – Optimization Methods in Management Science (Spring 2007) Recitation 1, February 8 th and February 9 th , 2007 Problem 1: Production Planning for PepsiCo The Wall Street Journal announced on February 1 st that at PepsiCo, the bottling company for Pepsi, profits were flat over the past few quarters. They call on you, a top OR student, to help change this stagnation. PepsiCo Company owns two different bottling plants that output different amounts of product for each hour run. If they run Plant 1 for a full hour, they will produce a certain number of cases of Pepsi, Sierra Mist, and Strawberry Fanta Light. PepsiCo must produce at least 12 tons of Pepsi, 8 tons of Sierra Mist, and 24 tons of Strawberry Fanta Light per day. It costs $20,000 per hour to run Plant 1, and costs and $16,000 per hour to run Plant 2. Each plant can be run for any amount between 0 and 8 hours per day. In one hour each plant produces the following tonnage: Pepsi Sierra Mist Diet Strawberry Fanta Plant 1 3 1 2 Plant 2 1 1 6 Part A: How can PepsiCo meet the requirements of the parent company at the lowest cost? Part B: Say there is an added constraint that Diet Strawberry Fanta can not make up more then 40% of the output, can we still model this as an LP?
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This note was uploaded on 01/17/2012 for the course MGMT 15.053 taught by Professor Jamesorli during the Spring '07 term at MIT.

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