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)
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:
Feed Type A
Feed Type B
Calories (per lb)
Vitamins (units per lb)
Cost (per lb)
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
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.