iPhone Sensitivity Analyses which all follow the same e first.) l. A small firm
ID: 357669 • Letter: I
Question
iPhone Sensitivity Analyses which all follow the same e first.) l. A small firm makes consisting per unit; product B requires 10 minutes of milling. 4,minutes f terest ideas requires 8 minutes of milling, 4 minutes for inspection, and 16 minutes of drilling. The department has 20 [ drilling per unit, and ours available during the next period for milling, 15 hours for inspection, and 24 hours for drilling. Product A contributes $2.40 per unit to profit, B contributes $2.50 per unit, and C contributes $2.5 per unit. The aim is to maximize profit. The computer solution of the problem is provided below hegg Final Reduced Objective Allowable Allowable Cell SC$2 XI SDS2 X2 SES2 X3 Name Coefficient Increase 0 0.620833333 24 0.620833333 IE+30 ook Constraint Allowable Name R.H. Side Increase Decrease BS6 Milling LHS SBS7 Inspection LHS SBS8 Drilling LHS 1200 0.20833333 520 1440 0.05208 3833 1200 900 1440 480 380 480 E+30 16k Formulate the LP model? what is the product mix? (or production quantities, or number of products produced) What are the basic and non-basic variables? a. c. What is the m d. A new competitor enterea the market providing product B with a competitive price, the manager decided to fio the company can make with current production?p the profit contribution of product B b S0.43 What is the effect of the manager decision? e. If the manager wants to produce product A. what change should be made to the objective function? f. Calculate tife range of optimality of product C and interpret the result. g. If the cost of product B increased by 0.25 and cost of product C decreased by 0.20? What is the effect on the tv optimal solution? Are there any non-binding constraints? Does it have a slack or surplus? Explain? The manager would like to make sure that the number of Product B produced not exceed 80% of the total h.Explanation / Answer
a)
Objective Variables
No of Product A = x1
No. pf Product B = x2
No. of Product C = X3
Constraint
1. Milling
12*x1+10*x2+8*x3 <= 20*60 --------1
2. Inspection
5*x1+ 4*x2 + 4*x3 <= 900-------2
3. Drilling
10*x1 + 8*x2 + 16*x3 <=1440 -------3
Objective Function
Max (Profit ) =Max( 2.4*x1 + 2.5*x2+ 2.5*x3 )
b)
Optimal Solution can be found in Final values of Variable
Basic variables - The variables with optimal solution of non zero values
Non Basic variables - Variables with zero final value in optimal solution
In this example :
Basic Variables - Product B & C
Non Basic Variables - Product A
c)
Profit = 2.4*x1 + 2.5*x2+ 2.5*x3
Optimal Solution
x1 = 0
x2 = 80
x3 = 50
putting this value in Profit equation
Profit = 325
d)
Profit contribution = Objective coefficient values of Variables
Currently for Product B, Profit contribution = 2.5
Allowable decrease for Objective coefficient i.e Profit contribution is 0.5321428
That means if we decrease in profit contibution of product B less than 0.5321428 , Optimal solution will be same
Product A = 0
Product B = 80
Product 3 = 50
Any decrease by value less than 0.5321428 will not change the optimal solution
As $4 < 0.5321428 so optimal solution will not change.
New Profit contribution of Product B = 2.5-0.4 = 2.1
Profit = 2.4*x1 + 2.1*x2+ 2.5*x3
Profit =2.4*0 + 2.1*80 + 2.5*50 = 293
e)
Allowable increase of objective coefficient of product A is 0.6208333
so increase of profit contribution for product A less than 0.6208333 will not change the existing optimal solution and product A will be not produced. To include the product A in optimal solution , profit contribution of product A should be increased by 0.620833
Increase of profit coefficent for product A >= 0.620833
Profit contribution of Product A>= (2.4+0.620833) >=3.0208333
f)
Range of optimality of Product C
Allowable increase = 2.5
Allowable decrease = 0.5
Current value of objective coefficeint of product C = 2.5
So range (2.5-0.5,(2.5+2.5) excluding the two value
Range =(2,5 )
(2 < Objective coefficent for product C <5) will not change the optimal solution
g) Cost of Product B is increased by 0.25 , That means Profit contribution of Product B is decreased by 0.25
New Profit Contribution of Product B = 2.5-0.25 = 2.25
Allowable decrease for objective coefficient i.e profit contribution of product B is 0.5321428
As decrease in profit contribution of B ,0.25 less than allowable decrease for B , it will not change optimal solution
Cost for Product C is decreased by 0.2 that means Profit contribution of Product C is Increased by 0.2
Allowable increase objective coefficient i.e profit contribution of product C is 2.5
As increase in profit contribution of C less than allowable increase for C , it will not change optimal solution
As 0.2 <2.5 so no change in optimal solution
So , as decrease in profit contribution of Product B and Increase profit contribution of Product C is within its allowable decrease and allowable increase respectively, the optimal solution will be same
Final Name Value Product A 0 Product B 80 Product C 50Related Questions
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