Problem 2: Rabbits and Chickens (25 marks)

A recent commerce graduate has found employment and purchased a condominium in Winnipeg. Since her monthly expenses are very close to her monthly net income, she has decided to raise rabbits and chickens on her balcony. She will be able to sell each rabbit at the farmers' market for $25 and each chicken for $15. Rabbits are sold 20 weeks after birth and chickens at 15 weeks after birth. Her balcony area is 12 square metres. Each rabbit requires 2 square metres and each chicken requires 0.5 square metres. Raising a rabbit costs $1/week for food and other minor things and chickens cost $0.60/week. The new graduate has $4.60/week that she can spend on raising these animals. Chickens become aggressive in a closed environment so she has learned that she will need to raise four times as many rabbits as chickens so that the rabbits can defend themselves. It may help you to consider a 60 week planning horizon.

Determine the number of each animal to raise in order to maximize the profit that she might realize form this imaginative venture. Ignore integer constraints.

1) (10 Marks) Formulate a linear model. Give clear definitions to your decision variables.

2) (10 Marks) Solve the problem graphically - show all the constraints and the objective function. Indicate the optimal solution on your graph.

3) (5 Marks) Set up a spreadsheet model. Use Solver to find the optimal solution.