Assignment 1

.pdf

School

Georgia Institute Of Technology *

*We aren’t endorsed by this school

Course

6481

Subject

Industrial Engineering

Date

Apr 3, 2024

Type

pdf

Pages

1

Uploaded by GeneralFlamingoPerson1028

Report
Homework 1 DNSC 4282/DNSC 6280 Supply Chain Analytics Professor Matta Due: January 25, 2024 Problem Set: (LP Formulation) 1. Formulate LP (10 points): Smitty’s is a clothing manufacturer that produces men’s shirts and pajamas. It has two primary resources available: sewing machine time and cutting machine time. Over the next month, Smitty can schedule up to 280 hours of work on sewing machines and up to 450 hours of work on cutting machines. Each shirt produced requires 1 hour of sewing time and 1.5 hours of cutting time. Producing each pair of pajamas requires 0.75 hour of sewing time and 2 hours of cutting time. Smitty’s accounting department analyzes cost and sales figures and states that each shirt produced will yield a $4 contribution profit and that each pair of pajamas will yield a $3 contribution profit. Formulate an LP that will maximize the contribution to profit from manufacturing shirts and pajamas. 2. Formulate LP (20 points): Coalco produces coal at three mines and ships it to four customers. The cost per ton of producing coal, the ash and sulfur content (per ton) of the coal, and the production capacity (in tons) for each mine are given in Table A. The number of tons of coal demanded by each customer are given in Table B. The cost (in dollars) of shipping a ton of coal from a mine to each customer is given in Table C. It is required that the total amount of coal shipped contain at most 5% ash and at most 4% sulfur. Formulate an LP that minimizes the cost of meeting customer demands. Table A: Production Requirements. Mine Production Cost ($) Capacity Ash Content (tons) Sulfur Content (tons) 1 50 120 0.08 0.05 2 55 100 0.06 0.04 3 62 140 0.04 0.03 Table B: Tons of Coal Demanded. Customer 1 Customer 2 Customer 3 Customer 4 80 70 60 90 Table C: Shipping Costs. Mine Customer 1 Customer 2 Customer 3 Customer 4 1 4 6 8 12 2 9 6 7 11 3 8 12 3 5 3. Formulate LP (10 points): Airborn Airlines is considering air service from its hub of operations in Cicely, Alaska, to Rome, Wisconsin, and Seattle, Washington. Airborn has one gate at the Cicely Airport which operates 12 hours per day. Each flight requires 1 hour of gate time. Each flight to Rome consumes 15 hours of pilot crew time and is expected to produce a profit of $2500. Serving Seattle uses 10 hours of pilot crew time per flight and will result in a profit of $2000 per flight. Pilot crew labor is limited to 150 hours per day. The market for service to Rome is limited to nine flights per day. Formulate an LP that maximizes the profit for Airborn.
Discover more documents: Sign up today!
Unlock a world of knowledge! Explore tailored content for a richer learning experience. Here's what you'll get:
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help