Question

4. 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.)

Please show the work pls ,thx

Answer 1

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 1

For Chickens,

Selling Price = 5 per dozen

Let x be the quantity of eggs sold in dozen

Breakeven is when Sales = Fixed + Variable Costs

5x = 580 + 2x

   3x = 580

Breakeven quantity, x= 580/3 = 193.33 dozens

For Ducks

Selling Price = 6 per dozen

Let y be the quantity of eggs sold in dozen

Breakeven sales; 6y = 640 + 1.556y

   4.444y = 640

Breakeven quantity, y = 640/4.444 = 144.014 dozens

Question 2

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 3

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

Question 4

Let the charge be c per dozen chicken eggs. For 12 months ;

Sales= c * (7 dozen/month )* 12 months= 84c

Variable cost = 14 * 12 =168

Fixed Cost = 580

Profit = 84c-168-580 = 84c-748

Profit of duck eggs in 12 month =54*12-14*12-640 = -160

84c -748 = -160

c= 588/84 = $7/ dozen chicken egg

Question 5

Let c be the charge per dozen chicken eggs. After 12 months

Sales= c * 7 * 12 =84c

Variable costs= 14*12 = 168

For breakeven , 84c = 168 + 580

c= 748/84 = $8.9/ dozen chicken eggs

Question 6

Similar to Question 5. Let d be the charge per dozen duck eggs. After 12 months

Sales= d* 9 *12 =108d

For breakeven, 108d= 168 +640

d = 808/108 = $7.48 per dozen duck eggs