Wald Press

Case Study: RED BRAND CANNERS

Purpose:

Decide Mount of tomato products to pack at this season.

Information:

1. Amount of Tomato: 3,000,000 pounds

2. Tomato quality: 20% (grade A) 80% (grade B)

3. Demand forcasts & selling prices (provided by sale manager):

Products Whole canned tomato Others

Demand no limitation Refer Exhibit 1

Selling prices has been set in light of the long-term marketing strategy of the company. Potential sales has been forcasted at these prices.

4. Purchasing price & product profitability (provided by controller)

Purchasing price: 6cents/pound Net profit: Refer Exhibit 2

5. Production requirement (provided by production manager)

Average point(quality) of tomato

Grade A Tomato Grade B tomato

9 points 5 points

Product Whole tommato Tomato juice Tomato paste

Minimum requirement 8 points 6 points 5 points (without grade A)

6. Vice president: 80,000 pounds of grade "A" tomatoes are available at

8.5 cents per pound.

7. Sale manager recomputes 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

Let

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.

PA = lbs of A-grade tomatoes in paste.

PB = lbs of B-grade tomatoes in paste.

Constraints :

WA WB JA JB PA PB

CWA CWB CJA CJB CPA CPB

1 1 ЎШ 14,400,000

1 1 ЎШ 1,000,000

1 1 ЎШ 2,000,000

1 1 1 ЎШ 600,000

1 1 1 ЎШ 24,00,000

1 -3 ЎЩ 0

3 -1 ЎЩ 0

Maximize CWA WA + CWB WB + CJA JA + CJB JB + CPA PA + CPBPB

Coefficients of Objective Function:

Both Cooper's and Myers' figures (Exhibits 2 and 3) are wrong.

Contribution = selling price - variable cost (excluding tomato cost)

Thus,

CWA = CWB = 1.48/18 = 0.0822

CJA = CJB = 1.32/20 = 0.066

CPA = CPB = 1.85/25 = 0.074

The contribution = $225,340 - $180,000 = $45,340.

Optimal primal solution

WA WB JA JB PA PB

525,000 175,000 75,000 225,000 0 2000,000

Optimal value = 225,340

Optimal dual solution

Column 7 8 9 10 11 12 13

Constraint 1 2 3 4 5 6 7

Value 0 0 0.0161 0.0903 0.0579 0.00810001 0.0081

Sensitivity on cost values

variable 1 2 3 4 5 6

Lower