Applied decision modeling.
Added on 2022-09-30
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Applied decision modeling
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Name of the student
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Project 1:
Let us consider, the Molokai Nut Company (MNC) needs to produce A
pound of chocolate-coated whole nuts (Whole), B pound of chocolate-
coated nut clusters (Cluster), C pound of chocolate-coated nut crunch bars
(Crunch), and D pound of plain roasted nuts (Roasted).
Hence, the decision variables are A, B, C and D.
Let us further consider P is the Profit that will be earned by the Molokai
Nut Company (MNC) from this operation.
Hence, the objective variable is P.
Now the given table is showing revenue and cost of each category of nuts.
Per Pound Revenue and Costs
Whole Cluster Crunch Roasted
Selling
Price
$5.00 $4.00 $3.20 $4.50
Variable
Cost
$3.15 $2.60 $2.16 $3.10
Hence, the total profit will be:
P = A*(5-3.15) + B*(4-2.60) + C*(3.20-2.16) + D*(4.50-3.10)
= 1.85*A + 1.40*B + 1.04*C + 1.40*D
Hence, the objective function will be
Max P = 1.85*A + 1.40*B + 1.04*C + 1.40*D
Now, the production unit has certain constraints as discussed below:
Constraint 1: Production Constraint
As per given information, below are the production constraints:
Let us consider, the Molokai Nut Company (MNC) needs to produce A
pound of chocolate-coated whole nuts (Whole), B pound of chocolate-
coated nut clusters (Cluster), C pound of chocolate-coated nut crunch bars
(Crunch), and D pound of plain roasted nuts (Roasted).
Hence, the decision variables are A, B, C and D.
Let us further consider P is the Profit that will be earned by the Molokai
Nut Company (MNC) from this operation.
Hence, the objective variable is P.
Now the given table is showing revenue and cost of each category of nuts.
Per Pound Revenue and Costs
Whole Cluster Crunch Roasted
Selling
Price
$5.00 $4.00 $3.20 $4.50
Variable
Cost
$3.15 $2.60 $2.16 $3.10
Hence, the total profit will be:
P = A*(5-3.15) + B*(4-2.60) + C*(3.20-2.16) + D*(4.50-3.10)
= 1.85*A + 1.40*B + 1.04*C + 1.40*D
Hence, the objective function will be
Max P = 1.85*A + 1.40*B + 1.04*C + 1.40*D
Now, the production unit has certain constraints as discussed below:
Constraint 1: Production Constraint
As per given information, below are the production constraints:
A >= 1000
400 <= B <= 500
C <= 150
D <= 200
Constraint 2: Machine hour Constraint
As per given information, each machine has maximum of 60 hours, that is,
3600 minutes’ time available. In addition, the following table is showing
required time, for producing per pound of each category products:
Minutes Required per Pound
Machine Whole Cluster Crunch Roasted
Hulling 1.00 1.00 1.00 1.00
Roasting 2.00 1.50 1.00 1.75
Coating 1.00 0.70 0.20 0.00
Packaging 2.50 1.60 1.25 1.00
Hence, the machine hour constraints will look like:
1*A + 1*B + 1*C + 1*D <= 3600
2*A + 1.5*B + 1*C + 1.75*D <= 3600
1*A + 0.70*B + 0.20*C + 0*D <= 3600
2.50*A + 1.60*B + 1.25*C + 1*D <= 3600
Constraint 3: Nuts and Chocolate Constraint
As per given information below are the nuts and chocolate constraints:
0.60*A + 0.40*B + 0.20*C + 1*D <= 1100
0.40*A + 0.60*B + 0.80*C + 0*D <= 800
Hence, the LP problem will look like:
400 <= B <= 500
C <= 150
D <= 200
Constraint 2: Machine hour Constraint
As per given information, each machine has maximum of 60 hours, that is,
3600 minutes’ time available. In addition, the following table is showing
required time, for producing per pound of each category products:
Minutes Required per Pound
Machine Whole Cluster Crunch Roasted
Hulling 1.00 1.00 1.00 1.00
Roasting 2.00 1.50 1.00 1.75
Coating 1.00 0.70 0.20 0.00
Packaging 2.50 1.60 1.25 1.00
Hence, the machine hour constraints will look like:
1*A + 1*B + 1*C + 1*D <= 3600
2*A + 1.5*B + 1*C + 1.75*D <= 3600
1*A + 0.70*B + 0.20*C + 0*D <= 3600
2.50*A + 1.60*B + 1.25*C + 1*D <= 3600
Constraint 3: Nuts and Chocolate Constraint
As per given information below are the nuts and chocolate constraints:
0.60*A + 0.40*B + 0.20*C + 1*D <= 1100
0.40*A + 0.60*B + 0.80*C + 0*D <= 800
Hence, the LP problem will look like:
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