Question

A business found the price of a fresh whole chicken to be as follows:

Weight in pounds of a Whole Chicken	5	6	7	8	9	10	11	12	13	14
Price per pound	1.20	1.15	1.05	1.00	0.95	0.90	0.86	0.80	0.75	0.69

a. Fit a linear trendline to the data, and identify this equation as a reasonable demand function.

b. State the revenue function that corresponds to this situation.

Assume the above business is willing to supply 25 pounds to a local restaurant at a price of $1.60 per pound and 20 pounds at a price of $1.45 per pound.

c. Find the supply function. Assume this is a linear function.

d. Using the supply and demand functions identified above, find the point of equilibrium.

e. At a price of $1.50, will there be a shortage of chicken or will there be a surplus of chicken? Why?

To produce the chickens, the business determines their variable costs to be $0.30 per pound and the fixed costs are $2.50.

f. Find the cost function.

g. Find the profit function.

h. Identify the break-even point(s).

Answer 1

Answer for a)

After Fitting a linear trendline to this data

We get Demand dunction line

P=1.44-0.05Q

Answer for b)

Revenue Fucntion

R=PQ=(1.44-0.05Q)*Q=1.44Q-0.05Q^2

Answer for c)

(y-1.6)/(x-25)=(1.6-1.45)/(25-20)

(y-1.6)/(x-25)=0.15/5=0.03

y-16=0.03x-0.75

y=0.03x+15.75 ( Y is Quantity and X is Price)

Q=0.03P+15.75

P=33.33Q-525

Answer for D)

We have an equillibrium when Supply meets demand

33.33Q-525=1.44-0.05Q

33.38Q=526.44

Q=526.44/33.38=15.7712 (Rounded to whole number)

P=33.33*15.7712-525=0.6514

P at Equillibrum 0.6514 and Q at equillibrium 15.7712 Pounds