Sunseel Industries produces two types of raw materials, A and B, with a production cost of $4 and $8 per unit, respectively. The processing times for A and B are observed to be 5 hours and 4 hours, respectively. A total of 3000 processing hours are available per month. The combined production of A and B must be at least 700 units per month. The factory is expected to produce at least 400 units of B and not more than 1200 units of A each month. Develop a linear program that Sunseel Industries can use to determine the number of units of each raw material to produce that will meet the demand and minimize the total cost. Let A = number of units of Raw material-A produced per month Let B = number of units of Raw material-B produced per month Write the LP in standard form: Min A + B subject to A + Bs 3000 (max processing hours) B 2 A (minimum total A + production)

Sunseel Industries produces two types of raw materials, A and B, with a production cost of $4 and $8 per unit, respectively. The processing times for A and B are observed to be 5 hours and 4 hours, respectively. A total of 3000 processing hours are available per month. The combined production of A and B must be at least 700 units per month. The factory is expected to produce at least 400 units of B and not more than 1200 units of A each month. Develop a linear program that Sunseel Industries can use to determine the number of units of each raw material to produce that will meet the demand and minimize the total cost. Let A = number of units of Raw material-A produced per month Let B = number of units of Raw material-B produced per month Write the LP in standard form: Min A + B subject to A + Bs 3000 (max processing hours) B 2 A (minimum total A + production)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 27EQ

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Equations and inequalities describe the relationship between two mathematical expressions.

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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

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Sunseel Industries produces two types of raw materials, A and B, with a production
cost of $4 and $8 per unit, respectively. The processing times for A and B are
observed to be 5 hours and 4 hours, respectively. A total of 3000 processing hours
are available per month. The combined production of A and B must be at least 700
units per month. The factory is expected to produce at least 400 units of B and not
more than 1200 units of A each month. Develop a linear program that Sunseel
Industries can use to determine the number of units of each raw material to produce
that will meet the demand and minimize the total cost.
Let A = number of units of Raw material-A produced per month
Let B = number of units of Raw material-B produced per month
Write the LP in standard form:
Min
A A+
A B
subject to
A +
Bs 3000 (max processing hours)
A +
B 2
(minimum total
production)
AI

Write the LP in standard form:
Min
A +
A B
subject to
AA A +
B< 3000 (max processing hours)
A +
В >
A (minimum total
production)
A (minimum production of B)
A s
A (maximum production of A)
А, В
A (non-negativity conditions)

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