Red Brand Canners Case Study

Problem 1: Structure this problem verbally, including a written description of the constraints and objective. What are the decision variables?

Problem Diagnostic

1. Availability of tomato crop

a. Total availability = 3,000,000 pounds

b. Grade A = 3,000,000 * 20% = 600,000 pounds

c. Grade B = 3,000,000 * 80% = 2,400,000 pounds

2. Demand forecast (focusing only tomato product)

Product | Demand forecast (cases) | Pounds per case | Total pound |

Whole tomato | 800,000 | 18 | 14,400,000 |

Tomato juice | 50,000 | 20 | 1,000,000 |

Tomato paste | 80,000 | 25 | 2,000,000 |

3. Crop quality

d. Grade A = 9 points per pound

e. Grade B = 5 points per pound

4. Product minimum average quality

f. Whole tomato = 8 points per pound (can be made from product grade A and B)

g. Tomato juice = 6 points per pound (can be made from product grade A and B)

h. Tomato paste = 5 points per pound (made only from product grade B)

5. Contribution margin

Product | Canned Whole Tomato | Tomato Juice | Tomato Paste |

Selling price | $4.00 | $4.50 | $3.80 |

Variable cost (Exclude tomato cost) | 2.52 | 3.18 | 1.95 |

Contribution margin | $1.48 | $1.32 | $3.80 |

6. Tomato cost

i. Average delivered price = $0.06 per pound

j. Total crop = 3,000,000 pounds

k. Total tomato cost = 3,000,000 * $0.06 = $180,000

l. Tomato juice = 6 points per pound (can be made from product grade A and B)

Decision Variables

Let WA = Weight of Grade A Tomato in Canned Whole Tomato

WB = Weight of Grade B Tomato in Canned Whole Tomato

JA = Weight of Grade A Tomato in Tomato Juice

JB = Weight of Grade B Tomato in Tomato Juice

PA = Weight of Grade A Tomato in Tomato Paste

PB = Weight of Grade B Tomato in Tomato Paste

Product | Canned Whole Tomato | Tomato Juice | Tomato Paste |

Grade A | WA | JA | PA |

Grade B | WB | JB | PB |

Problem 2: Develop a...