An urban farmer is pondering whether to invest in ducks or chickens to raise for eggs that she plans to sell to friends and neighbors. The materials needed to make a good henhouse and chicken run will cost $560. A simple setup for ducks will be slightly higher at $620 since they require water at all times. Ducklings and chicks are about the same in price — she figures that $20 will be needed to get four females of either species. A 50-pound sack of layer pellets costs $14 and water is essentially free. It will take the four hens a month to work their way through the sack of feed and during that time she can collect 84 eggs, which she plans to sell for $5 per dozen. Ducks eat at the same rate but lay eggs at a higher rate — in one month she believes she can collect 108 eggs. Duck eggs are also more highly prized by consumers; the urban farmer believes they will sell for $6 per dozen.

1) What is the break-even point for duck eggs? What is the break-even point for chicken eggs?

2) Suppose she decides to get both ducks and chickens, each receiving their own area in her backyard with separate housing. How many months after startup (assume that she buys mature birds that begin laying immediately) will profit from chickens equal profit from ducks?

3) Suppose she decides to get both ducks and chickens, each receiving their own area in her backyard with separate housing. Plot profit lines for both ventures over a three-year period and determine a range of output for which each venture is superior.

4) Suppose she decides to get both ducks and chickens, each receiving their own area in her backyard with separate housing. How much should the farmer charge for a dozen chicken eggs in order to make the profit from the chicken egg venture equal to the profit of the duck egg venture at the 12 month point of her operation? (Assume that she buys mature birds that begin laying immediately.)

5) Suppose she decides to get both ducks and chickens, each receiving their own area in her backyard with separate housing. How much should the farmer charge for a dozen chicken eggs in order to make the chicken egg venture break even at month 12? (Assume that she buys mature birds that begin laying immediately.)

6) Suppose she decides to get both ducks and chickens, each receiving their own area in her backyard with separate housing. How much should the farmer charge for a dozen duck eggs in order to make the duck egg venture break even at month 12? (Assume that she buys mature birds that begin laying immediately.)