Quiz -1(a) MBA (F&B) term 2 batch 8Name: Roll No: Q1. Consider the following LP problem. Max :Z = 14Q + 11R + 15T ( revenue)Subject to constraints:Sorting : 2.4Q + 3.0R + 4.0T 960 minutesCrushing: 2.5Q + 1.8R + 2.4T 607 minutesPacking: 12Q + 18R + 24T 3600 minutes ; all variables are non negativeThe Solver solution to the above problem is given below: Adjustable Cells

FinalReducedObjectiveAllowableAllowable

CellNameValueCostCoefficientIncreaseDecrease

$B$3qty prod Q1900141.6256.5

$C$3qty prod R0-0.25110.251E+30

$D$3qty prod T55015130.3333

Constraints

FinalShadowConstraintAllowableAllowable

CellNameValuePriceR.H. SideIncreaseDecrease

$F$5Sorting res used67609601E+30284

$F$6 Crushing res used6075607143247

$F$7packing res used36000.12536002089.811686.4

Answer the following: a) If a final iteration simplex table was made, what would be the values of the different variables in the objective function row. Draw a table and show it. b) Write the dual of the above problem and find the solution for the dual problem. c) Indicate the which of the constraints in the dual problem will be binding and which one will have surplus and by what amount. d) If the firm grants you additional 10 units of Crushing time, what will be the change in the profit and will there be any effect in the solution to the main problem. e) Which of the constraints in the main problem is binding and which one has excess resource. f) If the unit profit for product Q is decreased by 3 units and unit profit for product T is increased by 5 units which will be the net change in the solution of the main problem and consequential profits. g) If you told to return some of the resource which resource would you like to give up. h) If you were to ask for some additional resource which resource will would like to have. i) If sorting time is increased by 100 units and packing time is reduced by 100 units what will be the impact of the total profit. j) If a new product (S) is contemplated which requires 3 minutes of sorting , 4 minutes of crushing, and 10 units of packing time, what should be the least profit at which this product will be produced.

Quiz -1(b) MBA (F&B) term 2 batch 8Name: Roll No:Q1. Consider the following problem LP problem:MaxZ = 15A + 20B + 14C Subject to constraints :5A + 6B + 4C 210 -- C110A + 8B + 5C 200 C24A + 2B +5C 170 -- C3 ; all variables are non negativeAt a given iteration the simple table is as follows: ZABCS1S2S3RHS

1100-1.502.50500

0-2.500.251-0.75060

01.2510.6300.13025

01.503.750-0.251120

a) Find the optimal solution to the above problem. b) Write the dual problem and find its solution. c) Which product is not being produced and when will it be produced. d) Find the allowable increase and allowable decrease for constraint 2e) If a new product(D) is added which requires 2 units of C1 , 3 units of C2 and 2 units of C3 and the unit profit is 16 then should this product be produced. Give reasons for your answer.

Quiz -1(c) MBA (F&B) term 2 batch 8Name: Roll No:Q1. Consider the following problem LP problem:MaxZ = 10A + 6B + 5C Subject to constraints :2A + 3B + 4C 25 -- C1A + 3B + 2C 22 C26A + 3B +4C 32 -- C3 ; all variables are non negativeThe final iteration table is as given below ZABCS1S2S3RHS

1002.2000.4060

0001.601-0.801

0010.5300.406.67

0100.400-0.212

a) Find the allowable increase and allowable decrease for each of the coefficients in the objective function and each of the constraints. ( 8 marks) b) Write the dual of the above problem and find the solution to the same. ( 2 marks)

Quiz -1(d) MBA (F&B) term 2 batch 8Name: Roll No:Q1. Consider the following problem LP problem:MaxZ = 7A + 3B + 9C Subject to constraints :4A + 5B + 6C 360 -- C12A + 4B + 6C 300 C29A + 5B +6C 600 -- C3 ; all variables are non negativeAt a given iteration the simple table is as follows: ZABCS1S2S3RHS

10502-0.50570

010.500.5-0.5030

000.51-0.170.33040

00-2.50-3.52.5190

a) Is the above solution optimal. If not find the optimal solution. b) Write the dual of the above problem and find the solution of the same. c) Which product is not being produced and when will it be produced. d) Find the allowable increase and allowable decrease for constraint 1e) If a new product(D) is added which requires 2 units of C1 , 3 units of C2 and 2 units of C3 and the unit profit is 12 then should this product be produced. Give reasons for your answer.

Quiz -1(e) MBA (F&B) term 2 batch 8Name: Roll No:Q1. Consider the following problem LP problem:MaxZ = 12A + 15B + 14C Subject to constraints :3A + 5B + 8C 720 -- C12A + 3C 600 C24A + 6B +4C 640 -- C3 ; all variables are non negativeThe final iteration table is as given below ZABCS1S2S3RHS

103.200.4002.72016

000.1010.200-0.1548

00-3.100-0.201-0.35232

011.40-0.2000.40112

a) Find the allowable increase and allowable decrease for each of the coefficients in the objective function and each of the constraints. ( 6 marks) b) Write the dual of the above problem and find the solution to the same. ( 2 marks) c) If a new product is introduced which consumes 4 units of resource 1, 20 units of resource 2 and 6 units of resource 3 and give a unit profit of 10 ; then should this product be produced. Give your reasons. ( 2 marks)

Quiz -1(f) MBA (F&B) term 2 batch 8Name: Roll No:Q1. Solve the following LP problem using Simplex Method.

Min : Z = 1000A + 1200B Subject to constraints :5A + 4B 30 -- C17A + 6B 50 C23A + 8B 40 -- C3 ; all variables are non negative

Quiz -1(g) MBA (F&B) term 2 batch 8Name: Roll No:Q1.MaxZ = 12A + 10B + 15C + 11D Subject to constraints :5A + 3B + 4C +2D 240 -- C16A +8B + 2C+ 3D 240 C22A + 3B +3C +2D 180 -- C3 ; all variable are non negativeThe following is the final simplex table .ZABCDS1S2S3RHS

10.88.60000.604.60972

0-1.2-1.4100-0.400.6012

04.201.40010.40-1.6048

02.83.60100.60-0.4072

a) Bring out the sensitivity report showing the allowable increase and decrease for each of the objective coefficient and the resource constraints. ( 6 marks) b) Does this problem have multiple solution. Explain your reasons? ( 2 marks ) c) Write the dual of above problem and find its solution. ( 2 marks )

Quiz -1(h) MBA (F&B) term 2 batch 8Name: Roll No:Q1. Find the optimal solution to the following problem. Min : Z = 210A + 200B + 170C Subject to constraints :5A + 10B + 4C 15 -- C16A + 8B + 2C 20 C24A + 5B +5C 14 -- C3 ; all variables are non negative