produce the following styles of backpacks: (1) Settlement , (2) Dawson, and (3)
ID: 412615 • Letter: P
Question
produce the following styles of backpacks: (1) Settlement , (2) Dawson, and (3) Little America. Each backpack goes through four production stages: (1) cutting and coloring, (2) assembly, (3) finishing, (4) quality and packaging. The total number of hours available in each of these departments are 630, 600, 708, an d 135, respectively.
Each Settlement Backpack requires 0.7 hours of cutting and coloring, 0.5 hours of assembly, 1 hour of finishing, and 0.1 hours of quality and packaging. The corresponding numbers for each Dawson Backpack are 1 hour, 0.83 hours, 0.67 ho urs, and 0.25 hours, respectively. Likewise, the corresponding numbers for each Little America Backpack are 1 hour, 0.67 hours, 0.9 hours, and 0.4 hours, respectively.
The sales revenues for each type of backpack are as follows: Settlement $36.05, Dawson $ 39.50 , and Little America $43.30. The material costs are: Settlement $6.25, Dawson $7.50 , and Little America $8.50. The hourly cost of labor is $10 for cutting and coloring, $6 for assembly, $9 for finishing, and $8 for quality assurance and packaging.
Formulate an LP model
Explanation / Answer
In the given problem, the objective is profit maximization. We must decide on the product mix so that the company’s profit is maximized.
The decision variables for the LP are:
X1 = Number of bagpacks of Settlement Style
X2 = Number of bagpacks of Dawson Style
X3 = Number of bagpacks of Little America Style
The labour cost per unit of each style:
Settlement = (10*0.7)+(0.5*6)+(1*9)+(0.1*8) = $19.8/Unit
Dawson = (10*1)+(0.83*6)+(0.67*9)+(0.25*8)=$23.01/Unit
Little America = (10*1)+(0.67*6)+(0.9*9)+(0.4*8)=$25.32/Unit
Therefore, Total Cost/Unit of each style (Including Material Cost)
Settlement = (19.8+6.25) =$26.05 /Unit
Dawson=(23.01+7.50)=$30.51 /Unit
Little America= (25.32+8.50) = $33.82/Unit
Now, The Objective Function is :
Z= (36.05-26.05)X1+(39.50-30.51)X2+(43.30-33.82)X3
Subject to the following constraints:
Please note that these constraints are defined based on the maximum number of hours available for each of the four production stages: (1) cutting and coloring, (2) assembly, (3) finishing, (4) quality and packaging.
After forming the above described LP, MS Excel Solver could be used to get the values of X1, X2 and X3.( Which I suppose is not the scope of the question asked in this case)
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