Question 1 | Problem Set 2.1A | Chapter 2 | Modeling with Linear Programming | Operations Research

Описание: Question 1 | Problem Set 2.1A | Chapter 2 | Modeling with Linear Programming | Operations Research

Question No 01 | Problem Set 2.1A | Chapter 2 | Modeling with Linear Programming | Operations Research

Book Name : Operations Research: An Introduction

By : Hamdy A. Taha


Chapter Number : 02
Chapter Name : Modeling with Linear Programming

Lecture Number : 03
By (Name) : Awais Rasool

Exercise Number : 2.1A
Problems Number: 2.1A

Question Number : 01
Part Number : All Part

Example Number : 00
Theorem Number: 00
Awais Rasool Shah

Topics Name :
2.1 Two-Variable LP Model
2.2 Graphical LP Solution
2.2.1 Solution of a Maximization Model
2.2.2 Solution of a Minimization Model
12.3 Selected LP Applications
2.3.1 Urban Planning
2.3.2 Currency Arbitrage
2.3.3 Investment
2.3.4 Production Planning and Inventory Control
2.3.5 Blending and Refining
2.3.6 Manpower Planning
2.3.7 Additional Applications
2.4 Computer Solution with Excel Solver and AMPL
2.4.1 lP Solution with Excel Solver
2.4.2 LP Solution with AMPl

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Question No: 01
For the Reddy Mikks model, construct each of the following constraints and express it with a linear left-hand side and a constant right-hand side:
𝑥_1="Tons produced daily of exterior paint".
𝑥_2="Tons produced daily of interior paint".

𝑥_1="Tons produced daily of exterior paint".
𝑥_2="Tons produced daily of interior paint".
Part (𝑎):
The daily demand for interior paint exceeds that of exterior paint by
at least 1 ton.
Solution:
𝑥_2−𝑥_1≥1
Part (𝑏):
The daily usage of raw material 𝑀_2 in tons is at most 6 and at least 3. Solution:
𝑀_2=𝑥_1+2𝑥_2
𝑀_2≤6 and 𝑀_2≥3
𝑥_1+2𝑥_2≤6
𝑥_1+2𝑥_2≥3
𝑥_1="Tons produced daily of exterior paint".
𝑥_2="Tons produced daily of interior paint".
Part (𝑐):
The demand for interior paint cannot be less than the demand for exterior
paint.
Solution:
𝑥_2≥𝑥_1
𝑥_2−𝑥_1≥0  𝑥_1−𝑥_2≤0
Part (𝑑):
The minimum quantity that should be produced of both the interior and
the exterior paint is 3 tons.
Solution:
𝑥_1+𝑥_2≥3

𝑥_1="Tons produced daily of exterior paint".
𝑥_2="Tons produced daily of interior paint".
Part (𝑑):
The proportion of interior paint to the total production of both interior
and exterior paints must not exceed .5.
Solution:
𝑥_2:𝑥_1+𝑥_2≤0.5
𝑥_2/(𝑥_1+𝑥_2 )≤0.5
𝑥_2≤0.5(𝑥_1+𝑥_2)
𝑥_2≤0.5𝑥_1+0.5𝑥_2
𝑥_2−0.5𝑥_1−0.5𝑥_2≤0
0.5𝑥_2−0.5𝑥_1≤0
0.5𝑥_1−0.5𝑥_2≥0