Supply of a product increases according to the model.

Question

Supply of the product increases according to the model S(p) = aln(p-b) thousand units per week at a price of p dollars per unit. Suppliers are first willing to provide the product when it is priced at 10 dollars per unit (in the sense that when p = 10, S(p) = 0). When charging 20 dollars per item, suppliers provide 3 thousand items per week.

(a) Find the values of the constants a and b in the supply function formula.

(b) What is the mathematical domain of S? What is the practical domain of S? Are these the same?

Answer 1

a) When S(10) = 0 , 10-b must equal 1, assuming a≠0.

10-b = 1

b = 9

3 = a ln(20-9)

a = 3/ln(11) ≈ 1.25

b)

Mathematical domain: (9,∞)

Practical domain:[10,∞) (Can't produce negative units)

Not the same.