A manufacturer of clothing makes pants, shirts, and jackets. The
profit on a pair of pants is $12.00, on a shirt is $8.00, and on a
jacket is $18.00. Both pants, shirts and jackets require the work
of sewing operators and cutters. There are 60 hours of sewing
operator time and 48 hours of cutter time available. It takes 10
minutes to sew one pair of pants, 6 minutes to sew a shirt, and 14
minutes to sew one jacket. Cutters take 6 minutes on pants, 8
minutes on shirts, and 10 minutes on a jacket. Furthermore, each
item should undergo a final quality control inspection. An
inspection takes 1 minute on pants, 2 minutes on shirts, and 3
minutes on a jacket. There are 12 hours of quality control operator
time available.
The problem is to find the maximum profit and the amount of pants,
shirts and jackets to maximize the profit.
1) Write the linear programming model.
2) Find the optimal solution using Excel Solver.
Answer to the following questions without solving again the
model:
3) What will be the impact of increasing the number of producing
one additional shirt?
4) Assume that the new profit on a jacket is $30. Find the new
optimal solution and profit.
5) Management is considering adding an extra 50 minutes labor time.
Would you recommend adding this time to sewing, cutting, or quality
control? (Provide a detailed justification of your
recommendation).
First, we design the model:
Decision variables :
P = no. of pants to produce
S = no.of shirts to produce
J = no.of jackets to produce
Objective function :
Z (MAX) = 12P + 8S + 18J
Constraints :
Sewing operator 10P + 6S + 14J <= 3600
Cutter 6P + 8S + 10J <= 2880
Quality inspection 1P + 2S + 3J <= 720
Non negavtivity P,S,J>=0
Now, we put the model in Excel
Here, sumproduct is between the constraints/objective and the solution statement.
Now we go to DATA -- SOLVER :
Click OK
Here is the result :
Sensitivity report is as follows:
Now, we answer the questions from the information in the sensitivity report:
3) Producing an additional shirt will cost us $0.25. So, the profit will reduce.
4) If profit on Jacket is now $30. the optimal solution will remain the same. New profit will be: $7290
Old profit + additional profit on jacket i.e.(30-18)*225
= 4590 + 2700 = $7290
5) Extra minutes can be added to the sewing operator. It has the highest Lagrange Multiplier value. As we add 50minutes to sewing operator, the profit increases by 50minutes*1.125 = $56.25
New profit will be $4646.25
A manufacturer of clothing makes pants, shirts, and jackets. The profit on a pair of pants is $12...
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