Red Brand Canners – Case Study
REPORT ON RED BRAND CANNERS – CASE STUDY
Introduction:
Red Brand Canners is a medium sized company that cans and distributes a variety of fruit and vegetable products under private brands in the western states. The company makes three different tomato products including whole tomatoes, tomato juice and tomato paste. They also distribute Choice peach halves, peach nectarine and cooking apple products.
As part of their discussion over the amount of tomato products to pack in a particular season , it was observed that 3 million pounds of tomatoes are available for packing and distributing. This included two kinds of tomatoes ‘Grade A’ which constituted 20% of available crop and ‘Grade B’ being the remaining.
Problem Statement:
The problem can be divided into the following parts:
(a) How to allocate 3 million pounds of tomatoes in order to maximize profits?
(b) Should the company purchase additional Grade ‘A’ tomatoes? if so, what is the maximum amount the company can purchase and also formulate the new optimum product mix
Analysis
(A) Optimal Solution:
The objective is to maximize the profit by obtaining an optimal mix of Grade A and Grade B tomatoes. Hence, the problem can be formulated algebraically as below:
.
Where: si : selling price li : pounds of tomatoes used vi : variable costs per case of ith product xai : Amounts of Grade A in pounds used in ith product. xbi : Amounts of Grade A in pounds used in ith product.
The problem can be solved using excel solver solution of the same has been given in Appendix A.
Also, solving the problem using Lingo, we obtain:
MAX = xa1 + xb1 + xa1 -
3*xa2
xa1 + xa2 + xa3 + xa1 > xa2 > xa3 > xb1 > xb2 > xb3 >
Maximum Profit: 53340 $ xa1: 525000 lbs xb1: 175000 lbs xa2: 75000 lbs xb2: 225000 lbs xa3: 0.000000 lbs xb3: 2000000 lbs
(B) Coopers Solution:
Cooper agreed that the company would do well on the tomato crop, and that the incremental profit on whole
Introduction:
Red Brand Canners is a medium sized company that cans and distributes a variety of fruit and vegetable products under private brands in the western states. The company makes three different tomato products including whole tomatoes, tomato juice and tomato paste. They also distribute Choice peach halves, peach nectarine and cooking apple products.
As part of their discussion over the amount of tomato products to pack in a particular season , it was observed that 3 million pounds of tomatoes are available for packing and distributing. This included two kinds of tomatoes ‘Grade A’ which constituted 20% of available crop and ‘Grade B’ being the remaining.
Problem Statement:
The problem can be divided into the following parts:
(a) How to allocate 3 million pounds of tomatoes in order to maximize profits?
(b) Should the company purchase additional Grade ‘A’ tomatoes? if so, what is the maximum amount the company can purchase and also formulate the new optimum product mix
Analysis
(A) Optimal Solution:
The objective is to maximize the profit by obtaining an optimal mix of Grade A and Grade B tomatoes. Hence, the problem can be formulated algebraically as below:
.
Where: si : selling price li : pounds of tomatoes used vi : variable costs per case of ith product xai : Amounts of Grade A in pounds used in ith product. xbi : Amounts of Grade A in pounds used in ith product.
The problem can be solved using excel solver solution of the same has been given in Appendix A.
Also, solving the problem using Lingo, we obtain:
MAX = xa1 + xb1 + xa1 -
3*xa2
xa1 + xa2 + xa3 + xa1 > xa2 > xa3 > xb1 > xb2 > xb3 >
Maximum Profit: 53340 $ xa1: 525000 lbs xb1: 175000 lbs xa2: 75000 lbs xb2: 225000 lbs xa3: 0.000000 lbs xb3: 2000000 lbs
(B) Coopers Solution:
Cooper agreed that the company would do well on the tomato crop, and that the incremental profit on whole