A factory is producing three different type of product X, Y and Z. Each unit of product X, Y and Z requires 2 hour of labor, 2 hours of labor and 1 hours of labor respectively. Each unit of product X, Y and Z requires 1 hour of Machine, (-2) hour of Machine and 5 hours of Machine respectively. Each unit of product X, Y and Z requires 10kg of material, 5kg of material and 4kg of material respectively. Factory has maximum 100 hours of labor, 80 hours of Machine and 300 Kg of Material. What combination of three type of product produce that maximize profit with in a given constraints, if per unit profit on product X is Rs.2, per unit profit on product Y is Rs.12 and per unit profit on product Z is Rs.8. i. Find the solution using simplex method of linear programming. Interpret the initial table. Why slack variable is added in structural constraints? Interpret the meaning of slack variable if X = Y = Z = 15 units ii. i.

A factory is producing three different type of product X, Y and Z. Each unit of product X, Y and Z requires 2 hour of labor, 2 hours of labor and 1 hours of labor respectively. Each unit of product X, Y and Z requires 1 hour of Machine, (-2) hour of Machine and 5 hours of Machine respectively. Each unit of product X, Y and Z requires 10kg of material, 5kg of material and 4kg of material respectively. Factory has maximum 100 hours of labor, 80 hours of Machine and 300 Kg of Material. What combination of three type of product produce that maximize profit with in a given constraints, if per unit profit on product X is Rs.2, per unit profit on product Y is Rs.12 and per unit profit on product Z is Rs.8. i. Find the solution using simplex method of linear programming. Interpret the initial table. Why slack variable is added in structural constraints? Interpret the meaning of slack variable if X = Y = Z = 15 units ii. i.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

A factory is producing three different type of product X, Y and Z. Each
unit of product X, Y and Z requires 2 hour of labor, 2 hours of labor and 1
hours of labor respectively. Each unit of product X, Y and Z requires 1
hour of Machine, (-2) hour of Machine and 5 hours of Machine
respectively. Each unit of product X, Y and Z requires 10kg of material,
5kg of material and 4kg of material respectively. Factory has maximum
100 hours of labor, 80 hours of Machine and 300 Kg of Material. What
combination of three type of product produce that maximize profit with in
a given constraints, if per unit profit on product X is Rs.2, per unit profit
on product Y is Rs.12 and per unit profit on product Z is Rs.8.
i.
Find the solution using simplex method of linear programming.
Interpret the initial table.
Why slack variable is added in structural constraints? Interpret
the meaning of slack variable if X = Y = Z = 15 units
ii.
i.

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