red brand canners
TRANSCRIPT
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
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.