Question

of fans is now 170? Can we speculate the new profit value 9. If the number of cooling coils is now 420, what is the new profic? Bags Production problem ht Hand Side easibility) A manufacturer produces 3 models of bags: A, B and C. Constraints limitations (time available in minutes) in each of the 3 There is also one more constraint that requires the m A. The linear programmin production capacity Cutting, Sewing, and Packaging g model and the solution output are presented below: nge within w ce is applica lution and th ange Max 3A +5B +40 12A +10B+8C 18,000 15A +15B 12C 18,000 3A +4B 2C IA Cutting Sewing Packaging Model A 9,000 Variable 1E+30 1000 Model B E+30 4 1E.30 Value Price 14000 18000 Constraint 0 6000...- Cutting (LHS) Sewing (LHS) Packaging (LHS) 18000 1E 30 ease 5200- 1000 1000 1000 Model A LHS 1. What is the profit contribution of each model? 2. How much time does it take to pack one bag of model B?

how to solve this

Answer 1

Q1 : The profit contribution of each model is the Objective Coefficient of each model. Hence profit contribution of Model A is $3, Model B is $5 and Model C is $4.

Q2 : Time taken to pack one bag of model B is the coefficient of B is the equation corresponding to the packaging constraint. This equation is 3A+4B+2C. The coefficient of B in this equation is 4. Hence it takes 4 mins to pack one bag of model B.

Q3 : Available time for packaging is the Constraint R.H Side of the Packaging. We can see that this value is 9000. Hence available time for packaging is 9000 minutes.

Q4 : The number of bags of each model to be produced is given by the final value of the variables Model A, B and C. Thus 1000 bags of Model A, 200 bags of Model B and 0 bags of Model C should be produced to maximize profit. The optimal profit is given by substituting these values in the Objective Function equation which is 3A+5B+4C. Hence optimal profit in this case is given as 3*1000+5*200+4*0 = 3000+1000+0 = $4000. Optimal profit is thus $4000.

Q5 : The constraint were Final value is equal to Constraint R.H Side are binding. We can see that this occurs in case of Sewing Time and Model A minimum Production. Hence Sewing Time and Minimum 1000 bags of Model A are binding.

Q6 : The shadow price for Sewing is 0.33. That means for every 1 minute less available for sewing, the profit reduces by 0.33. If the sewing machine broke down for 50 hours or 50*60 = 3000 minutes, the profit would reduce by 3000*0.33 = $990

Q7 : The shadow price for Sewing is 0.33. That means for every 1 minute more available for sewing, the profit increases by 0.33. If overtime rate is $12 per hour then per minute rate is $0.2 per minute. As the increase in profit is more than the overtime rate, I would recommend to use overtime in this department.

Q8 : The shadow price for Model A constraint is -2. That means for every 1 additional bag to be produced of Model A, the profit reduces by 2. If 10 additional bags of A needs to be produced, the profit would reduce by 10*2 = $20

Q9 : As we can see the reduced cost and final value for Model C is 0. This means that there is atleast 1 more optimal solution for this scenario. In this optimal solution, Model C will have a final value of non-zero.

Q10 : We can see that the allowable increase for Model B is 1E+30 which is a very large number. This means that the optimal solution will stay the same irrespective of how much the profit contribution of Model B increases. Hence the optimal solution would not change and remain the same even if Model B profit increase by $1.