Essay About Demand Forcasts And Cwa Wa

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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
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 :
14,400,000
1,000,000
2,000,000
600,000
24,00,000
Maximize CWA WA + CWB WB + CJA JA + CJB JB + CPA PA + CPBPB
Coefficients of Objective Function:
Both Coopers 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
525,000
175,000
75,000
225,000
2000,000
Optimal value = 225,340
Optimal dual solution
Column
Constraint
Value
0.0161
0.0903
0.0579
0.00810001
0.0081
Sensitivity on cost values
variable
Lower