Faculty: Prof J Jha

Three types of tomato products.

Whole canned tomato

Tomato Juice

Tomato Paste

Total Quantity

(already

contracted/purchased)

Cost per lb* in US ¢

(1 lb = 453.592 gms)

*Libra Pondo (lb) (Latin)

Total Cost in US $

( 1 $ = 100¢)

3M Lbs 06 1,80,000

Types of

tomato

Quantity (in M

lbs)

Quality (in points) Quality points acceptable for

products

Grade A 0.6 9 Whole Canned - 8

Grade B 2.4 5 Juice - 6

Variables Particulars SP per case

(in $)/ lbs per

case

Contribution per lb

(in $)

AW A grade/whole canned

4.0/18 (1.48/18) = 0.0822 BW B grade/whole canned

AJ A grade/juice

4.5/20 (1.32/20) = 0.066 BJ B grade/juice

AP A grade/paste

3.80/25 (1.85/25) = 0.074 BP B grade/paste

Since the fruit has already been contracted,

The cost of fruit per pack is taken as a Sunk Cost

Max: Z = 0.0822*(AW+BW) + 0.066*(AJ+BJ)

+ 0.074*(AP+BP)

Demand constraints (lbs)

AW + BW <= 8,00,000 (Pre-determined because of quality of fruit available)

AJ + BJ <= 10,00,000 (50000 cases * 20 lbs/case)

AP + BP <= 20,00,000 (80000 cases * 25 lbs/case)

Quality constraints

For whole canned tomato

9AW + 5BW >= 8(AW + BW)

Solving, 1AW – 3BW >= 0

For tomato juice

9AW + 5BW >= 6(AW + BW)

Solving, 3AW – 1BW >= 0

For tomato paste . No constraints since paste is acceptable with B grade fruits.

Quantity constraints

For A Grade

AW + AJ + AP <= 6,00,000

(since only 0.6M lbs available)

For B Grade

BW + BA + BP <= 24,00,000

(Balance out of 3.0M lbs)

AW BW AJ BA AP BP Contribution profit

525000 175000 75000 225000 0 2000000

225340

45340

0.0822 0.0822 0.066 0.066 0.074 0.074

TOTAL QUANTITY

AW BW AJ BA AP BP USED AVAILABLE

DEMAND CANNED

TOMATOES 1 1 0 0 0 0 700000 800000

JUICE 0 0 1 1 0 0 300000 1000000

PASTE 0 0 0 0 1 1 2000000 2000000

QUALITY CANNED

TOMATOES 1 -3 0 0 0 0 0 0

JUICE 0 0 3 -1 0 0 0 0

QUANTITY A GRADE 1 0 1 0 1 0 600000 600000

B GRADE 0 1 0 1 0 1 2400000 2400000

AW BW AJ BA AP BP contribution profit

615000 205000 65000 195000 0 2000000 232564 45764

0.0822 0.0822 0.066 0.066 0.074 0.074

Total Quantity USED AVAILABLE

CANNED

TOMATOES 1 1 0 0 0 0 820000 880000

JUICE 0 0 1 1 0 0 260000 1000000

PASTE 0 0 0 0 1 1 2000000 2000000

CANNED

TOMATOES 1 -3 0 0 0 0 0 0

JUICE 0 0 3 -1 0 0 0 0

A GRADE 1 0 1 0 1 0 680000 680000

B GRADE 0 1 0 1 0 1 2400000 2400000

• Gross Profit with 3.0M lbs= $ 45340.

• Gross Profit with 3.08M lbs= $ 45764.

• That translates into a situation

wherein the company can earn more

profit if it procures 80000 lbs of A

grade tomato @ 8.5¢/lb, thereby,

earning an extra profit of US$ 424.