Quiz 3

SA305 – Linear Programming
Asst. Prof. Nelson Uhan
Spring 2016
Quiz 3
Instructions. You have 15 minutes to complete this quiz. You may not use any other materials (e.g., notes, homework,
Problem 1. You have been recently hired as the new operations research analyst for the Simplex Furniture Company,
which builds two types of dining tables: basic and deluxe. The tables are assembled from two components: tops and
legs. Each basic table consists of 2 tops and 4 legs, and takes 0.25 hours to assemble. Each deluxe table consists of 3 tops
and 5 legs, and takes 0.50 hours to assemble. The components need to be fabricated before being used to assemble a
table: it takes 0.10 hours to fabricate a top, and 0.15 hours to fabricate a leg. Simplex has 200 hours of assembly time and
75 hours of fabrication time available. Basic tables are sold at a profit of $50 each, and deluxe tables are sold at a profit
of $80 each. Simplex would like to maximize its profits from dining tables, assuming all tables assembled are sold.
Your predecessor left you with a linear program he started for this problem, with the following decision variables:
B = number of basic tables assembled
D = number of deluxe tables assembled
T = number of tops fabricated
L = number of legs fabricated
The linear program contains the following constraints and an accompanying note:
B = 2T + 4L
D = 3T + 5L
(relationship between number of tables assembled
and number of components needed)
a. (10 points) Explain why your predecessor’s constraints are incorrect.
b. (10 points) Fix your predecessor’s constraints: write a set of constraints that correctly models the relationship
between the number of tables assembled and the number of components needed.