hw1 - Introduction to Optimization MS&E 111/ENGR 62 Spring...

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Introduction to Optimization MS&E 111/ENGR 62, Spring 2015-2016, Stanford University Instructor: Ashish Goel Homework 1. Given 4/7/16. Due 4/14/16 at 1:00PM (at the Huang HW Cabinet) Problem 1 A chicken farmer is trying to decide what to use as feed and is considering using a combination of feeds from local suppliers. The farmer would like to feed the chickens at minimum cost while making sure the chickens get an adequate supply of calories and vitamins. The cost, calorie content, and vitamin supply of each feed is given in the table below: Contents Feed Type A Feed Type B Calories (per lb) 500 700 Vitamins (units per lb) 50 25 Cost (per lb) $1 $2 Each chicken requires at least 600 calories per day and 40 units of vitamins. As an additional constraint, the farmer would like at least half of the diet to consist of feed type B for public relations purposes. (a) Formulate this problem as a linear program. Clearly indicate your decision variables, your objective function, and your constraints. (b) Solve this in Excel. Attach the Answer Report to your HW. Be sure to indicate on it if you worked with anyone else. Problem 2 A company produces two kinds of products. A product of the first type requires 1/4 hours of assembly labor, 1/8 hours of testing, and $1.20 worth of raw materials. A product of the second type requires 1/3 hours of assembly, 1/3 hours of testing, and $0.90 worth of raw materials. Given the current personnel of the company, there can be at most 90 hours of assembly labor and 80 hours of testing each day.

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