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# Red brand canners

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### Red brand canners

1. 1. RED BRAND CANNERS<br />-Jay Prakash Jain [11BM60033]<br /> -Srinjoy Saha [11BM60075]<br /> -Sovan Nayak [11BM60077]<br /> -Pritam Datta [11BM60107]<br /> -Abhishek Ranjan [11BM60117]<br />
2. 2. Problem Statement<br />How to allocate the already purchased tomatoes among the three tomato products in order to maximize profit?<br /> Should the company purchase additional Grade A tomatoes at a price of .085\$ per lb? As stated in case, company wishes to purchase 80,000 lbs of Grade A tomatoes, what is the new optimum product mix?<br />What is the maximum amount the company can purchase? <br />
3. 3. Variables<br />All variables are in pounds<br />
4. 4. Basic LP Model <br />max 0.0822X11 + 0.0822X12 + 0.066X21 + 0.066X22 + 0.074X31 + 0.074X32<br />subject to<br />X11 + X12 <=800000…… Resource Constraint for Whole Canned Tomato<br />X21 + X22 <=1000000…… Resource Constraint for Tomato Juice<br />X31 + X32 <=2000000…….Resource Constraint for Tomato Paste<br />X11 + X21 + X31 <=600000……Resource Constraint for Grade A Tomato<br />X12 + X22 + X32 <=2400000……. Resource Constraint for Grade B Tomato<br />-X11 +3X12 <=0………. Grade Constraint for Whole Canned Tomato<br />-3X21 + X22 <=0………. Grade Constraint for Tomato Juice<br />
5. 5. Optimum Product Mix from <br />The Basic LP Model <br />
6. 6. Refined Basic LP Model<br />With Coopers Table <br />max 0.02222X11 + 0.02222X12 + 0.0066675X21 + 0.0066667X22 + 0.014X31 + 0.014X32<br />subject to<br />X11 + X12 <=800000…… Resource Constraint for Whole Canned Tomato<br />X21 + X22 <=1000000…… Resource Constraint for Tomato Juice<br />X31 + X32 <=2000000…….Resource Constraint for Tomato Paste<br />X11 + X21 + X31 <=600000……Resource Constraint for Grade A Tomato<br />X12 + X22 + X32 <=2400000……. Resource Constraint for Grade B Tomato<br />-X11 +3X12 <=0………. Grade Constraint for Whole Canned Tomato<br />-3X21 + X22 <=0………. Grade Constraint for Tomato Juice<br />
7. 7. Refined Optimum Product Mix <br />based on Coopers Table <br />
8. 8. Unit Worth of a Resource <br />based on Basic Model<br />min 1800000y1 + 1000000y2 + 2000000y3 + 600000y4 + 2400000y5 + 0y6 + 0y7<br />subject to<br />y1 + y4 - y6 >=0.0822<br />y1 + y5 + 3y6 >=0.0822<br />y2 + y4 - 3y7 >=0.066<br />y2 + y5 + y7 >=0.066<br />y4 + y3 >=0.074<br />y3 + y5 >=0.074<br />
9. 9. Unit Worths for resources <br />based on Basic Model<br />
10. 10. Unit Worth of a Resource <br />based on Basic Model<br />After adding the extra Grade A tomato<br />min 1800000y1 + 1000000y2 + 2000000y3 + 680000y4 + 2400000y5 + 0y6 + 0y7<br />subject to<br />y1 + y4 - y6 >=0.0822<br />y1 + y5 + 3y6 >=0.0822<br />y2 + y4 - 3y7 >=0.066<br />y2 + y5 + y7 >=0.066<br />y4 + y3 >=0.074<br />y3 + y5 >=0.074<br />
11. 11. Unit Worths for resources <br />based on Basic Model <br />after adding the entire lot of Grade A tomatoes<br />
12. 12. Unit Worth of a Resource <br />based on Coopers Table<br />min 1800000y1 + 1000000y2 + 2000000y3 + 600000y4 + 2400000y5 + 0y6 + 0y7<br />subject to<br />y1 + y4 - y6 >=0.0222<br />y1 + y5 + 3y6 >=0.0222<br />y2 + y4 - 3y7 >=0.0066<br />y2 + y5 + y7 >=0.0066<br />y4 + y3 >=0.014<br />y3 + y5 >=0.014<br />
13. 13. Unit Worths for resources <br />based on Coopers Table<br />
14. 14. LP Model <br />With Myers Table <br />max -0.00006X11 - 0.00006X12 + 0.004X21 + 0.004X22 + 0.022X31 + 0.022X32<br />subject to<br />X11 + X12 <=800000…… Resource Constraint for Whole Canned Tomato<br />X21 + X22 <=1000000…… Resource Constraint for Tomato Juice<br />X31 + X32 <=2000000…….Resource Constraint for Tomato Paste<br />X11 + X21 + X31 <=600000……Resource Constraint for Grade A Tomato<br />X12 + X22 + X32 <=2400000……. Resource Constraint for Grade B Tomato<br />-X11 +3X12 <=0………. Grade Constraint for Whole Canned Tomato<br />-3X21 + X22 <=0………. Grade Constraint for Tomato Juice<br />
15. 15. Optimum Product Mix from <br />The Mayers LP Model <br />
16. 16. Observations<br />1. As we can see that the Coopers Model is not using the entire lot of raw material which we have with us , as a result of that we will have to bear an inventory cost equivalent to the cost price of 0.2 million pounds of Grade B tomato which will ultimately minimize the effect of the net contribution.<br />2. Also, we found that if we follow Coopers Model we have a shadow price a 2.9 cent per extra pound of added Grade A tomato. Where as using the basic model we can get the same shadow price at 9.03 cent.<br />3. And finally, for the Coopers model Raw Material cost which is a fixed cost or sunk cost for this period under consideration has been used to calculate total variable cost for each and every product line which is faultyfrom the concept of optimization as well as contribution.<br />4. Although we are getting the max profit while following Myers model , we will not be using this. As Myers Model is following a different cost price model for the raw material which is not viable at this point time as the company has already signed the deal @ 6 cent per pound.<br />
17. 17. Decisions<br />1. We will be using Basic Model and keep on producing the products as per the optimum product mix we have got based on this model.<br />Also we will Buy Grade A tomatoes @8.5 cent per pound as Suggested by Gordon as we have seen each extra pound Grade A will help me earn an extra 9.03 cent . Also from the shadow price table where we have used the entire 80000 pound of grade A tomatoes , we can see that the shadow price is still 9.03 cent. So, buying the entire 800000 pound will be a profitable decision. <br />(NOTE: If we keep on adding grade A tomatoes, at a level of 11.9 lakh/12.0 lakh pound this 9.03 cent will start falling . That’s where we can get the first diminishing Step of shadow price.)<br />3. From the next season the pricing contract for raw material should follow Myers Model as it is providing the highest profit under the constraints. <br />