A business found the price of a fresh whole chicken to be as follows: Weight in
ID: 1149539 • Letter: A
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).
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
Explanation / Answer
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
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