2. D.G.H.M. Inc. makes two different grades of cement mix for driveway paving for their clients. Many of the jobs they do are seasonal, but some are unaffected by weather. The mixes, referred to as Rough, and Smooth are made by combining different percentages of the same three ingredients as listed below. Rough has a popularity for things like land fill and basements walls, whereas Smooth is significantly more popular for floors, garages and walkways. Mix\Ingredients | limestone | silica sand Silk Selling Price (per pound) Rough Smooth 80% 25% 10% 30% 10% 45% $3.55 $5.60 The ingredients (Limestone and Silica Sand) are purchased from a vendor in another province to avoid marketing competition and as such they have to be shipped in. The final shipping costs per load are indicated in'the following table Ingredients Pounds per shipment | Cost per Shipment Pounds available Limestone 250 $650 1000 Silica Sand Silk 400 $300 $400 2400 100 3000

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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2. D.G.H.M. Inc. makes two different grades of cement mix for driveway paving for their clients.
Many of the jobs they do are seasonal, but some are unaffected by weather. The mixes,
referred to as Rough, and Smooth are made by combining different percentages of the same
three ingredients as listed below. Rough has a popularity for things like land fill and basements
walls, whereas Smooth is significantly more popular for floors, garages and walkways.
Mix\Ingredients limestone silica sand Silk Selling Price (per pound)
Rough
%08
30%
10%
10%
45%
$3.55
$5.60
Smooth
25%
The ingredients (Limestone and Silica Sand) are purchased from a vendor in another province
to avoid marketing competition and as such they have to be shipped in. The final shipping
costs per load are indicated in'the following table
Ingredients Pounds per shipment | Cost per Shipment | Pounds available
Limestone
Silica Sand
Silk
$650
$300
$400
250
1000
2400
400
100
3000
In a recent marketing survey, D.G.H.M. Inc. has determined that over the next year they want
to manufacture between 1000 and 2250 pounds of Rough cement; and at least 1500 pounds
of Smooth cement. They also want to make sure that the amount of Smooth cement is never
less than that of double the amount of Rough cement. If X is the number of pounds of Rough
cement manufactured and Y is the number of pounds of Smooth cement manufactured, what
combination of X and Y (integer only solutions) would maximize the company profits.
For this problem clearly derive the Linear program
Graph this problem and clearly indicate the feasible options
• Clearly determine the solution to the problem using the method of points (be smart about
which points you have to evalate based on the graph of the objective function
Create a excel spread sheet, use solver to solve it and discuss/interpret the dual values
and range of optimality for all constraints and coefficients. What does these range of
optinailities tell ns?
Discuss the results of this question froim a business perspective involving the constraints
given.
Transcribed Image Text:2. D.G.H.M. Inc. makes two different grades of cement mix for driveway paving for their clients. Many of the jobs they do are seasonal, but some are unaffected by weather. The mixes, referred to as Rough, and Smooth are made by combining different percentages of the same three ingredients as listed below. Rough has a popularity for things like land fill and basements walls, whereas Smooth is significantly more popular for floors, garages and walkways. Mix\Ingredients limestone silica sand Silk Selling Price (per pound) Rough %08 30% 10% 10% 45% $3.55 $5.60 Smooth 25% The ingredients (Limestone and Silica Sand) are purchased from a vendor in another province to avoid marketing competition and as such they have to be shipped in. The final shipping costs per load are indicated in'the following table Ingredients Pounds per shipment | Cost per Shipment | Pounds available Limestone Silica Sand Silk $650 $300 $400 250 1000 2400 400 100 3000 In a recent marketing survey, D.G.H.M. Inc. has determined that over the next year they want to manufacture between 1000 and 2250 pounds of Rough cement; and at least 1500 pounds of Smooth cement. They also want to make sure that the amount of Smooth cement is never less than that of double the amount of Rough cement. If X is the number of pounds of Rough cement manufactured and Y is the number of pounds of Smooth cement manufactured, what combination of X and Y (integer only solutions) would maximize the company profits. For this problem clearly derive the Linear program Graph this problem and clearly indicate the feasible options • Clearly determine the solution to the problem using the method of points (be smart about which points you have to evalate based on the graph of the objective function Create a excel spread sheet, use solver to solve it and discuss/interpret the dual values and range of optimality for all constraints and coefficients. What does these range of optinailities tell ns? Discuss the results of this question froim a business perspective involving the constraints given.
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