QT Assignment

RED BRAND CANNERSTotal number of tomatoes, T = 3,000,000

Grade ‘A’ tomatoes, A = 20% of 3,000,000 = 600,000

Grade ‘B’ tomatoes, B = 80% of 3,000,000 =2,400,000

Cost Price, cp= $0.06

Calculating the demand of Tomatoes in the form of various products

1. Whole tomatoes = X = 800,000 casesEach case of whole tomatoes = 18 poundsTotal pounds of whole tomatoes demanded = 18 x 800,000 = 1,440,000 pounds

2. Tomato juice = Y = 50,000 casesEach case of tomato juice = 20 poundsTotal pounds of tomato juice demanded = 20 x 50,000 = 1,000,000 pounds

3. Tomato paste = Z = 80,000 casesEach case of tomato paste = 25 poundsTotal pounds of tomato paste demanded = 25 x 80,000 = 2,000,000 pounds

Composition of Various Tomato products in terms of type of tomatoes

1. Whole tomatoes = X1 and X2 where A and B signify the respective grades

The quality of whole tomatoes can be given by equation9(X1) + 5(X2) = 8(X1+X2)where 9,5 and 8 show the rating of the tomatoes=> X1 – 3X2 = 0 & X1 + X2 ≤ 1440000

2. Tomato Juice = Y1 and Y2

Tomato Juice production as per demand = 1,000,000 pounds

The quality of Tomato juice can be given by the equation9(Y1) + 5(Y2) = 6(Y1 + Y2)=> 3Y1 – Y2 = 0 & Y1 + Y2 ≤ 1,000,000

3. Tomato paste = Z1 and Z2

Tomato paste production as per demand = 2,000,000 pounds

=> Z1 + Z2 ≤ 2,000,000There are no quality constraints

Contribution without taking tomatoes into account

1. Whole tomatoes = $4 - $2.52 = $1.48/18 = P1

2. Tomato Juice = $4.5 - $3.18 = $1.32/20 = P2

3. Tomato Z1ste = $4.8 - $2.95 = $1.85/25 = P3

CASE 1:

Objective Function:

P1(X1 + X2) + P2(Y1 +Y2) + P3(Z1+Z2) – 180,000

Constraints:

X1 X2 Y1 Y2 Z1 Z2 Constraints

1 1 <=1440000

0 1 1 <= 1000000 1 1 <= 2000000 1 1 1 <= 600000 1 1 1 <= 2400000 1 -3 >= 0 3 -1 >= 0 1 >= 0

Answer Report:

Target Cell (Max)

Cell NameOriginal Value Final Value

$E$23 Profit X1 0 225200

Adjustable Cells


$E$5Quantity X1 0 525000

$F$5Quantity X2 0 175000

$G$5Quantity Y1 0 75000

$H$5Quantity Y2 0 225000

$I$5Quantity Z1 0 0

$J$5Quantity Z2 0 2000000

ConstraintsCell Name Cell Value Formula Status Slack

$K$16 Used 0

$K$16>=$M$16 Binding 0

$K$17 Used 2000000

$K$17>=$M$17

Not Binding 2000000

$K$10 Used 700000

$K$10<=$M$10

Not Binding

13700000

$K$11 Used 300000

$K$11<=$M$11

Not Binding 700000

$K$12 Used 2000000

$K$12<=$M$12 Binding 0

$K$13 Used 600000


$K$14 Used 2400000


$K$15 Used 0

$K$15>=$M$15 Binding 0

Sensitivity Report:

Adjustable Cells

FinalReduce

d Objective AlloX1ble AlloX1ble

Cell Name Value CostCoefficie

nt Increase Decrease

$E$5Quantity X1 525000 0 0.082

0.154666667

0.021333333

$F$5Quantity X2 175000 0 0.082 0.464

0.021333333

$G$5Quantity Y1 75000 0 0.066

0.021333333

0.154666667

$H$5Quantity Y2 225000 0 0.066

0.014222222

0.051555556

$I$5Quantity Z1 0 -0.032 0.074 0.032 1E+30

$J$5Quantity Z2

2000000 0 0.074 1E+30 0.016

Constraints

FinalShado

wConstrai

nt AlloX1ble AlloX1bleCell Name Value Price R.H. Side Increase Decrease

$K$16 Used 0 -0.008 0 1400000 200000$K$17 Used

2000000 0 0 2000000 1E+30

$K$10 Used 700000 0

14400000 1E+30 13700000

$K$11 Used 300000 0 1000000 1E+30 700000$K$12 Used

2000000 0.016 2000000 200000

466666.6667

$K$13 Used 600000 0.09 600000 600000

466666.6667

$K$14 Used

2400000 0.058 2400000

466666.6667 200000

$K$15 Used 0 -0.008 0

466666.6667 600000

CASE 2:

Objective Function:

P1(X1 + X2) + P2(Y1 +Y2) + P3(Z1+Z2) – 180,000 – 6,800

Constraints:

X1 X2 Y1 Y2 Z1 Z2

1 1 <=1448000

0

1 1 <= 1000000 1 1 <= 2000000

1 1 1 <= 680000 1 1 1 <= 2400000

1 -3 >= 0 3 -1 >= 0 1 >= 0

Answer Report:

Target Cell (Max)


$D$24 Profit X1 0 232400

Adjustable Cells


$D$6Quantity X1 0 615000

$E$6Quantity X2 0 205000

$F$6Quantity Y1 0 65000

$G$6Quantity Y2 0 195000

$H$6Quantity Z1 0 0

$I$6Quantity Z2 0 2000000

ConstraintsCell Name Cell Value Formula Status Slack

$J$11 Used 820000$J$11<=$L$11

Not Binding

13660000

$J$12 Used 260000$J$12<=$L$12

Not Binding 740000

$J$13 Used 2000000$J$13<=$L$13 Binding 0

$J$14 Used 680000$J$14<=$L$14 Binding 0

$J$15 Used 2400000$J$15<=$L$15 Binding 0

$J$16 Used1.16415E-

10$J$16>=$L$16 Binding 0

$J$17 Used 0$J$17>=$L$17 Binding 0

$J$18 Used 2000000$J$18>=$L$18

Not Binding 2000000

Sensitivity Report:

Adjustable Cells

FinalReduce

d Objective AlloX1ble AlloX1ble

Cell Name Value CostCoefficie

nt Increase Decrease$D$6

Quantity X1 615000 0 0.082

0.154666667

0.021333333

$E$6Quantity X2 205000 0 0.082 0.464

0.021333333

$F$6Quantity Y1 65000 0 0.066

0.021333333

0.154666667

$G$6

Quantity Y2 195000 0 0.066

0.014222222

0.051555556

$H$6

Quantity Z1 0 -0.032 0.074 0.032 1E+30

$I$6Quantity Z2 2000000 0 0.074 1E+30 0.016

Constraints

FinalShado

wConstrain

t AlloX1ble AlloX1bleCell Name Value Price R.H. Side Increase Decrease

$J$11 Used 820000 0 14480000 1E+30 13660000$J$12 Used 260000 0 1000000 1E+30 740000$J$13 Used 2000000 0.016 2000000

173333.3333

493333.3333

$J$14 Used 680000 0.09 680000 520000

546666.6667

$J$15 Used 2400000 0.058 2400000

493333.3333

173333.3333

$J$16 Used

1.16415E-10 -0.008 0

546666.6667 520000

$J$1 Used 0 -0.008 0 1480000 173333.333

7 3$J$18 Used 2000000 0 0 2000000 1E+30

CONCLUSION

With earlier quantity of tomatoes profits are less i.e.

Total Cont. 225200Raw Material 180000Profit 45200

Now with additional 80000 pounds @ 8.5 cents/pound scenario is:

Total Cont. 232400Raw Material 186800Profit 45600

So, its profitable to get extra 80000 pounds of tomatoes even at higher rate.

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QT Assignment