Red Brand Canners

Case Study: RED BRAND CANNERS
Vice President of Operations Mr. Michell Gorden Controller Mr. William Copper Sale Manager Mr. Charles Myers Production Manager Mr. Dan Tucker

Purpose: Decide the amount of tomato products to pack at this season. Tomato Products Whole Tomato Tomato Juice Tomato Paste

Information: 1. Amount of Tomato: 3,000,000 pounds to be delivered. Tomato quality: 20% (grade A) × 3,000,000 = 600,000 pounds 80% (grade B) × 3,000,000 = 2,400,000 pounds (provided by production manager)

2. Demand forecasts & selling prices (provided by sale manager):

Products Demand

Whole canned tomato no limitation

Others Refer Exhibit 1

1

lbs.

correction (800,000/18) = 44444.5 Cases

Selling prices has been set in light of the long-term marketing strategy of the company. Potential sales have been forecasted at these prices. 3. Purchasing price & product profitability (provided by controller) Purchasing price 6cents/pound Net profit Refer Exhibit 2

Grade A 9 points

Grade B 5 points

Product
Minimum requirement

Whole tomato 8 points

Tomato juice 6 points

Tomato paste

5 points (without grade A)

2

3.8 -(0.54+0.26+0.38+0.77) = 1.85 4.0-(1.18+0.24+0.4+0.7) = 1.48

4.5 - (1.32+0.36+0.85+0.65) = 1.32

0.3

5. 80,000 pounds of grade "A" tomatoes are available at 8.5 cents per pound. (provided by the Vice president of operations) 6. Sale manager re-computes the marginal profits (Exhibit 3).

Linear Programming Solutions
(a) How to use the crop of 3,000,000 lbs. of tomatoes? (b) Whether to purchase an additional 80,000 lbs. of A-grade tomatoes?

Part (a)
Formulation: WA = lbs. of A-grade tomatoes in whole. WB = lbs. of B-grade tomatoes in whole. JA = lbs. of A-grade tomatoes in juice. JB = lbs. of B-grade tomatoes in juice.

3

¸Ñ(1) (2) ¤§Áp¥ß¤èµ{¦¡
1 CASE = 0.0518* 25= 1.295

1 CASE = [(0.0932*(3/4)+0.0518*(1/4)]*18

PA = lbs. of A-grade tomatoes in paste. PB = lbs. of B-grade tomatoes in paste.