manufacturingand marketing data for a production situation. there are 3 departme

Question

manufacturingand marketing data for a production situation. there are 3 departments: punch, welding, assembly. there are also 3 products: a,b,c. product A passing punch department for 2 hours and in the assembly department for 5 hours. product B passing punch department for 3 hours and in welding department for 2.5 hours. product C passing punch department for 2 hours and in the welding department for 1.5 hours and in the assembly department for 2.5 hours. capacity of punch department is 1200 hours, capacity of welding department is 600 hours, and capacity of assembly department is 1500 hours. the objective is to determine the quantity of product A,B,and C to produce so that total profit will be maximized. the profit for product A is 0.6, product B is 0.7, and product C is 0.5
question: how many A,B,C products should be sold for maximum benefit? manufacturingand marketing data for a production situation. there are 3 departments: punch, welding, assembly. there are also 3 products: a,b,c. product A passing punch department for 2 hours and in the assembly department for 5 hours. product B passing punch department for 3 hours and in welding department for 2.5 hours. product C passing punch department for 2 hours and in the welding department for 1.5 hours and in the assembly department for 2.5 hours. capacity of punch department is 1200 hours, capacity of welding department is 600 hours, and capacity of assembly department is 1500 hours. the objective is to determine the quantity of product A,B,and C to produce so that total profit will be maximized. the profit for product A is 0.6, product B is 0.7, and product C is 0.5
question: how many A,B,C products should be sold for maximum benefit?
question: how many A,B,C products should be sold for maximum benefit?

Explanation / Answer

Solution :

In this problem profit is mentioned .So this problem is of maximization.

Let X 1 be the decision variable for For Product A

Let X 2 be the decision variable for For Product B

Let X 3 be the decision variable for For Product C

Z be the objective equation.

So LPP Formulation will be as follows

Maximization Z = 0.6 X1 + 0.7 X2 + 0.5 X3

Subject to

2X1+3X2+2X3<=1200 (Punch Department Constraint)

2.5X2+1.5X3<=600 (Welding Constraint)

5X1+2.5X3<=1500 (Assembly Constraint)

Solution to above LPP by Simplex Method

Tableau #1
x1 x2 x3 s1 s2 s3 z   
2 3 2 1 0 0 0 1200   
0 2.5 1.5 0 1 0 0 600
5 0 2.5 0 0 1 0 1500   
-0.6 -0.7 -0.5 0 0 0 1 0

Tableau #2
x1 x2 x3 s1 s2 s3 z   
2 0 0.2 1 -1.2 0 0 480
0 1 0.6 0 0.4 0 0 240
5 0 2.5 0 0 1 0 1500   
-0.6 0 -0.08 0 0.28 0 1 168

Tableau #3
x1 x2 x3 s1 s2 s3 z   
1 0 0.1 0.5 -0.6 0 0 240
0 1 0.6 0 0.4 0 0 240
0 0 2 -2.5 3 1 0 300
0 0 -0.02 0.3 -0.08 0 1 312

Tableau #4
x1 x2 x3 s1 s2 s3 z   
1 0 0.5 0 0 0.2 0 300   
0 1 0.333333 0.333333 0 -0.133333 0 200   
0 0 0.666667 -0.833333 1 0.333333 0 100   
0 0 0.0333333 0.233333 0 0.0266667 1 320   

Optimal Solution:

z = 320;

A= x1 = 300

B=x2 = 200

C=x3 = 0

Departments Products Capacity in hours A B C Punch 2 3 2 1200 Welding 2.5 1.5 600 Assembly. 5 2.5 1500

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