Four products are processed sequentially on three machines. The following table
ID: 3568746 • Letter: F
Question
Four products are processed sequentially on three machines. The following table gives the pertinent data of the problem.
Manufacturing time (hr) per unit
Machine
Cost per hr ($)
Product 1
Product 2
Product 3
Product4
Capacity (hr)
1
10
2
3
4
2
500
2
5
3
2
1
2
380
3
4
7
3
2
1
450
Unit selling price ($)
75
70
55
45
a) Formulate the problem as an Linear programming model, and find the optimum solution.
Four products are processed sequentially on three machines. The following table gives the pertinent data of the problem.
Manufacturing time (hr) per unit
Machine
Cost per hr ($)
Product 1
Product 2
Product 3
Product4
Capacity (hr)
1
10
2
3
4
2
500
2
5
3
2
1
2
380
3
4
7
3
2
1
450
Unit selling price ($)
75
70
55
45
Explanation / Answer
Let the number of product 1 be, a
Let the number of product 2 be, b
Let the number of product 3 be, c
Let the number of product 3 be, d
(Objective Function): Z=75*a + 70*b + 55*c + 45*d
Now,
We have to maximize this objective function keeping in mind the followoing Constraints.
20*a +30*b +40*c +20*d <=500 (For Machince 1)
15*a + 10*b + 5*c + 10*d <=380 (For Machince 2)
48*a + 12*b + 8*c + 4*d <=450 (For Machince 3)
a,b,c,d>=0 (Variable Constraint)
Now we have to solve the above Linear programing model to maximize the value of objective function.
This can be done using Simplex Algorithm:
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