Question

Question text

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.

1. 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?
2. 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

ANSWER::

For Chickens,

Fixed Cost = Henhouse set up cost + Cost of purchasing Chicks

= 560 + 20 = 580

Variable Cost = pellet cost = 14 for 84 eggs

   = 14 for 7 dozens

   = 2 per dozen Eggs

Similarly For Ducks,

Fixed cost = 620 + 20 = 640

Variable Cost = 14 for 108 eggs = 1.556 per dozen

Question (A)

Let m be the number of months

Profit from chicken = sales per month * m - 14*m - 580

sales per month = quantity * price = 7 dozens * 5 = $ 35

$14 is the variable cost per month, 580 is the fixed cost

So, Profit from chicken = 35m-14m-580

Similarly,

Profit from ducks = 54m-14m-640

( sales is 9 dozens(108 eggs) * 6$ per month , ie 54 $ per month)

Profit from chcken= profit from Ducks

35m-14m-580 = 54m-14m-640

19m = 640-580

m= 3.16 months

Profits from both startups will be equal after 3.16 months

Question (B)

Plot is given in the image. 36 months are plotted. use the formula obtained from Question 2 to find profits (21m -580 for chickens and 40m-640 for ducks).

Chicken is superior for first 3 months. Duck is superior for next 33 months

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