Please check and correct my answers. Thank you.

Question

Jack Benny can get blood from a stone. If he has x stones, the number of pints of blood he can extract from them is f(x) = 2x^(1/3). Stones cost Jack w dollars each. Jack can sell each pint of blood for p dollars.

a) How many stones does Jack need to extract y pints of blood?

b) What is the cost of extracting y pints of blood?

c) What is Jack’s supply function when stones cost w each? When stones cost $8 each?

d) If Jack has 19 relatives who can also get blood from a stone in the same way, what is the aggregate supply function for blood, Y, when stones cost w dollars each?

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my answers:

a)
y^3/8

b)
(w)(y^3/8)

c)
S(p,w) = (8p/3w)^(1/2)
S(p) = (p/3)^(1/2)

d)
Y = 20(8p/3w)^(1/2)