Question

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 cost $560. A simple setup for ducks is slightly higher, or $620, because they require water at all times. Ducklings and chicks are about the same in price—she figures that $20 is 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. She plans to sell them 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. Because duck eggs are more highly prized by consumers, the urban farmer believes they will sell for $6 per dozen.

a. 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?
b. 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. Then, determine the range of output for when each venture is superior.

Answer 1

The profit from chickens will equal the profit from ducks after the same number of months, but both options currently result in a loss. Therefore, the urban farmer will not make a profit from either option.

Step-by-step explanation:

To determine when the profit from chickens will equal the profit from ducks, we need to calculate the costs and revenues for both options. Let's start with the chickens:

Total cost for materials for the henhouse and chicken run: $560

Cost to purchase four female chicks: $20

Cost of feed for one month: $14

Total revenue from selling eggs: $5 per dozen x 7 dozen = $35

Profit from chickens: Revenue - Costs = $35 - ($560 + $20 + $14) = -$559

Now let's calculate the costs and revenues for the ducks:

Total cost for materials for the duck setup: $620

Cost to purchase four female ducklings: $20

Cost of feed for one month: $14

Total revenue from selling eggs: $6 per dozen x 9 dozen = $54

Profit from ducks: Revenue - Costs = $54 - ($620 + $20 + $14) = -$600

As we can see, both options currently result in a loss. To find out how many months it will take for the profit from chickens to equal the profit from ducks, we can set up an equation: Profit from chickens x months = Profit from ducks x months. Since the profits are negative, the equation becomes: (-559) x months = (-600) x months. This means that the profit from chickens will equal the profit from ducks after the same number of months.

Therefore, it will never happen because the profits are both negative. The urban farmer will not make a profit from either option.