A winery has the following capacity to produce an exclusive dinner wine at eithe
ID: 419707 • Letter: A
Question
A winery has the following capacity to produce an exclusive dinner wine at either of its two vineyards: Vineyard 1 has supply of 3,500 bottles at a cost of $23 each; Vineyard 2 has supply of 3,100 bottles at a cost of $25 each. Four Italian restaurants around the country are interested in purchasing this wine. Because this wine is exclusive, they all want to buy as much as they need but will take whatever they can get. The maximum amounts required by the restaurants and the prices they are willing to pay are as follows: Restaurant 1 will purchase up to 1,800 bottles at $69 each; Restaurant 2 will purchase up to 2,300 bottles at $67 each; Restaurant 3 will purchase 1,250 bottles at $70 each; and Restaurant 4 will purchase up to 1,750 bottles at $66 each. The costs of shipping a bottle from the vineyards to the restaurants are summarized in the following table. Construct and solve a Linear Optimization model that will maximize profit.
A. Answer the following questions about the optimal solution.
i. How many of the potential routes are being used?
ii. Is there excess capacity or unmet demand? If so, where?
iii. What are the high-priority allocations (if any exist)?
B. Run the Sensitivity Report for this model (label the report sheet ‘1b’). Answer the following questions:
i. If demand were to increase at any of the restaurants, which would be the most profitable? What is the explanation of this cost?
ii. Which of the unused routes would have to be reduced by the greatest amount to become part of the optimal solution?
Restaurant 1 Restaurant 2 Restaurant 3 Restaurant 4 Vineyard 1 $7 $8 $13 $9 Vineyard 2 $12 $6 $8 $7Explanation / Answer
RST1
RST2
RST3
RST4
SUPPLY
COST
VND1
7
8
13
9
3500
23
VND2
12
6
8
7
3100
25
DUMMY
0
0
0
0
500
0
DEMAND
1800
2300
1250
1750
SELLING PRICE
69
67
70
66
NOW THE NET PROFIT = SELLING PRICE – ( PRODUCTION COST + TRANSPORTATION COST )
THE NET PROFIT VALUE IS:
RST1
RST2
RST3
RST4
SUPPLY
VND1
39
36
34
34
3500
VND2
32
36
37
34
3100
DUMMY
0
0
0
0
500
DEMAND
1800
2300
1250
1750
OBJECTIVE FUNCTION:
MAXIMIZE Z = 39*11 + 36*12 +13 +14 +21 +36*22 +37*23 +34*24
A)
1.total number of allocation = 6
For solve the problem to find optimal solution we have to convert the profit table into cost table
RST1
RST2
RST3
RST4
SUPPLY
VND1
-39
-36
-34
-34
3500
VND2
-32
-36
-37
-34
3100
DUMMY
0
0
0
0
500
DEMAND
1800
2300
1250
1750
use Vogal's method to solve the problem
Allocated table
RST1
RST2
RST3
RST4
SUPPLY
VND1
2300
1200
3500
VND2
1300
1250
550
3100
DUMMY
500
500
DEMAND
1800
2300
1250
1750
2. Yes there is one unmated demand to restaurant 1.
3. In this case for optimal solution I have given highest priority to restaurant 2 from VND1.
B)
1. From the profit table it is clear that: the average profit from restaurant 2 is highest.
From restaurant 2 the average profit is $36
2. From the profit table: it is clear that the unused path from VEND2 to RST1 gives lowest profit, so I want to minimize the demand of RST1.
RST1
RST2
RST3
RST4
SUPPLY
COST
VND1
7
8
13
9
3500
23
VND2
12
6
8
7
3100
25
DUMMY
0
0
0
0
500
0
DEMAND
1800
2300
1250
1750
SELLING PRICE
69
67
70
66
NOW THE NET PROFIT = SELLING PRICE – ( PRODUCTION COST + TRANSPORTATION COST )
THE NET PROFIT VALUE IS:
RST1
RST2
RST3
RST4
SUPPLY
VND1
39
36
34
34
3500
VND2
32
36
37
34
3100
DUMMY
0
0
0
0
500
DEMAND
1800
2300
1250
1750
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