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: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.3: Rules For Addition
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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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