Business 2400 Assignment 1 Winter, 2017

1. A car assembly plant makes two types of cars, named the Avalon and the Bonavista. Each
Avalon gives a profit of $2000, while each Bonavista gives a profit of $3000. They must make at
least 250 Avalons. Each Avalon requires 3 labour-hours in Department 1, and 8 labour-hours in
Department 2. Each Bonavista requires one labour-hour in Department 1, and 15 labour-hours
in Department 2. Each week Department 1 is available for 3000 labour-hours, and Department
2 is available for 17,990 hours. At least 25% of the total production must be of Bonavistas.
(a) Formulate a linear optimization model for this situation. Write every constraint in standard
form (?, = , or ? a number), with a one or two word description of the purpose of the
constraint.
(b) Solve the model using a 1500 by 1500 grid, clearly indicating each constraint with a word
description next to it, the feasible region, the trial and optimal isovalue lines, and the point
of optimality. Compute the exact solution algebraically, and clearly state the recommendation and the OFV.
1500 Bonavistas 1000 500 0 0 500 1000
1 Avalons 1500 2. A machine shop makes pipes for the oil and gas industry in lengths of 240 cm and 400 cm. The
shorter pipes give a profit of $150 each, while each long pipe gives a profit of $270. They can
sell at most 900 of the 240 cm pipes and at most 800 of the longer ones. Each pipe spends time
on three machines as follows:
Minutes per Pipe Minutes
Machine Short
Long
Available
Lathe
5
7
4900
Polisher
8
2
4500
Grinder
10
8
7200
For every long pipe made, there must be at least two short pipes made. For every pair of long
pipes made, there can be at most five short pipes made.
(a) Formulate a model for this problem.
(b) Solve the model using Excel.
(c) State the recommendation. 2