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Q1:A/ The Office Supplies Company offers two types of pens, the first type has high specifications, while the second type has normal specifications. The expected profit from selling each unit of the first type is half a dollar, and from selling each unit of the second type is a quarter of a dollar. The time taken to manufacture the first type is twice the time taken to manufacture the second type for the purpose of producing no more than 1,000 pens of both types per week. The company can produce at most 400 units of the first type per week, and it can produce no more than 700 units of the second type per week. Note that the company can produce each of them separately. Required: Create the linear programming model to find the optimal production mix so that the company achieves the maximum possible profit.

Q1:A/ The Office Supplies Company offers two types of pens, the first type has high specifications, while the second type has normal specifications. The expected profit from selling each unit of the first type is half a dollar, and from selling each unit of the second type is a quarter of a dollar. The time taken to manufacture the first type is twice the time taken to manufacture the second type for the purpose of producing no more than 1,000 pens of both types per week. The company can produce at most 400 units of the first type per week, and it can produce no more than 700 units of the second type per week. Note that the company can produce each of them separately. Required: Create the linear programming model to find the optimal production mix so that the company achieves the maximum possible profit.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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Q1:A/ The Office Supplies Company offers two types of pens, the first type has high specifications, while the second type has normal specifications. The expected profit from selling each unit of the first type is half a dollar, and from selling each unit of the second type is a quarter of a dollar. The time taken to manufacture the first type is twice the time taken to manufacture the second type for the purpose of producing no more than 1,000 pens of both types per week. The company can produce at most 400 units of the first type per week, and it can produce no more than 700 units of the second type per week. Note that the company can produce each of them separately. Required: Create the linear programming model to find the optimal production mix so that the company achieves the maximum possible profit. B/ Put the following program in matrix standard form Min (z) = 10x₁+11x2 S.T. X₁+2x₂ ≤ 150 3x₁+4x₁ ≤200 36x1+x₂≤ 175 X₁ and x₂ non nagative with
Transcribed Image Text:Q1:A/ The Office Supplies Company offers two types of pens, the first type has high specifications, while the second type has normal specifications. The expected profit from selling each unit of the first type is half a dollar, and from selling each unit of the second type is a quarter of a dollar. The time taken to manufacture the first type is twice the time taken to manufacture the second type for the purpose of producing no more than 1,000 pens of both types per week. The company can produce at most 400 units of the first type per week, and it can produce no more than 700 units of the second type per week. Note that the company can produce each of them separately. Required: Create the linear programming model to find the optimal production mix so that the company achieves the maximum possible profit. B/ Put the following program in matrix standard form Min (z) = 10x₁+11x2 S.T. X₁+2x₂ ≤ 150 3x₁+4x₁ ≤200 36x1+x₂≤ 175 X₁ and x₂ non nagative with
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