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Question Homework1

The document contains instructions for homework 1 in ECEN 687. It includes 3 problems: 1) A furniture manufacturer problem to maximize revenue by determining an optimal product mix given lumber stock and production requirements. 2) A linear programming problem to determine the conditions on coefficients s and t that will make the problem have an optimal solution, be infeasible, or be unbounded. 3) A meat packing plant problem to maximize total net profit by determining how much of each product to sell fresh or smoked given production quantities and profit levels for each processing method.

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274 views1 page

Question Homework1

The document contains instructions for homework 1 in ECEN 687. It includes 3 problems: 1) A furniture manufacturer problem to maximize revenue by determining an optimal product mix given lumber stock and production requirements. 2) A linear programming problem to determine the conditions on coefficients s and t that will make the problem have an optimal solution, be infeasible, or be unbounded. 3) A meat packing plant problem to maximize total net profit by determining how much of each product to sell fresh or smoked given production quantities and profit levels for each processing method.

Uploaded by

suprajaconjeti
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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ECEN

687 Fall 2017 Homework 1



Due 4pm, September 8, Friday
Submission must be through ecampus
No late submission accepted!

1. (10 points) A furniture manufacturer has 3600 bd.ft. of Walnut, 4300 bd.ft. of Maple, and
6550 bd.ft. of Oak in stock. It can produce three products using this lumber, with input
requirement as below:
Wood needed (bd.ft./unit) Revenue/unit
walnut maple oak
Table 10 50 100 $100
Desk 10 30 40 $50
Chair 80 5 0 $10

A table is always sold in combination with 4 chairs; and a desk is always sold with one chair.
But a chair can be sold independently. Formulate the problem of finding product mix to
maximize revenue.

2. (10 points) Find necessary and sufficient condition for the values of s and t to make the LP
problem
Maximize x1 + x2
s.t. sx1 + tx2 1
x1, x2 0
a. have an optimal solution,
b. be infeasible,
c. be unbounded.

3. (10 points) A meat packing plant produces 480 hams, 400 pork bellies and 230 picnic hams
every day; each of these products can be sold either fresh or smoked. The total number of
hams, bellies and picnics that can be smoked during a normal working day is 420; in
addition, up to 250 products can be smoked on overtime at a higher cost. The net profit are
as follows.
Fresh Smoked regular Smoked overtime
Hams $8 $14 $11
Bellies $4 $12 $7
Picnics $4 $13 $9

Please formulate an LP problem that decides the amount of each such that the total net
profit is maximized.

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