Please help whit the next task, make sure to read all. I need and original produ
ID: 376987 • Letter: P
Question
Please help whit the next task, make sure to read all.
I need and original production problem with description and formulation, Cannot be coppied from a book or othe source,it can be any topic, I'll need complete answers and procedure please.
Im putting this as an example NO NEED TO BE ANSWER, Thank you
JC Corp. must determine their product mix and the best use of their workers to maximize their profits. They make four types of products: P1001, P2002, P3003, and P4004. Due to a quality problem with their main competitor, demand is at an all-time high (thus assumes all items produced will sell at the current prices). All products go through two operations: welding and assembly. The production times per product (in hours) and the per unit profit contribution are presented in the Table. There are 6 welding shop workers and 9 assembly area workers. Workers have a “capacity” of 36 hours per week. To maintain a diverse portfolio of products at least 25% of the total number of units produced must be of the sum of products 3003 and 4004. What should be their weekly production plan?
Probelm formulation
Decision Variables
P1001 = Units to be produced of type1001 per week
P2002 = Units to be produced of type 2002 per week
P3003 = Units to be produced of type 3003 per week
P4004 = Units to be produced of type 4004 per week
Objective Function
Maximize (Profits)
Profits = $90 × P1001 + $75 × P2002 + $60 × P3003 + $45 × P4004
Constraints
1.5 × P1001 + 3 × P2002 + 1.7 × P3003 + 2 × P4004 216
2.1 × P1001 + 1 × P2002 + 1.2 × P3003 + 3.5 × P4004 324
(P3003 + P4004) / T 25%
Pj: integer j S
Pj 0 j S
Type P1001 P2002 P3003 P4004 Welding ops (hrs) 1.5 3 1.7 2 Assembly ops (hrs) 2.1 1 1.2 3.5 Profit/Unit $90 $75 $60 $45Explanation / Answer
Problem
You being manager are trying to find a production plan for the upcoming week. There are 3 products say, P, Q, and Q to produce using 3 machines say A and B, C, and D. Each of the 4 machines performs a unique process Also There is 1 machine of each type, and each machine is available for 40 hours per week. The unit processing times for each machine is:
Table 1: Machine Data
Unit processing Time in hrs
Machine
Product P
Product Q
Product R
Availability (hrs)
A
20
10
10
40
B
12
28
16
40
C
15
6
16
40
D
10
15
0
40
Total Processing time
57
59
42
160
Storing the inventory from 1 week to the next is not permitted. The operating expenses are $6000/week, no matter how many components and products are made. The $6000 includes all expenses except for material costs. The unit revenues and maximum sales for the week are indicated as:
Table 2: Product Data
Item
Product P ($)
Product Q ($)
Product R ($)
Revenue per unit
90
100
70
Material cost per unit
45
40
20
Profit per unit
45
60
50
Maximum sales
100
40
60
Formulation
Objective is to maximize the profit
Profit = (90-45)P + (100-40)Q + (70-20)R – 6000
= 45P + 60Q + 50R – 6000
Since, operating cost is not a function of objective hence while calculating we can remove it.
Hence,
Objective
Zmax = 45P + 60Q + 50R
Subject to , (Constraints),
20P+10Q +10R 40 (Machine A)
12P+28Q+16R 40 (Machine B)
15P+6Q+16R 40 (Machine C )
10P+15Q+0R 40 (Machine D)
(Market constraints)
0 P 100
0 Q 40
0 R 60
Where,
P 0
Q 0
R 0
Unit processing Time in hrs
Machine
Product P
Product Q
Product R
Availability (hrs)
A
20
10
10
40
B
12
28
16
40
C
15
6
16
40
D
10
15
0
40
Total Processing time
57
59
42
160
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.