7. Supply of a product increases according to the model S(p) = a In(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 value of constants a and b in the supply function formula. (b) What is the mathematical domain of S? Is this different from the practical domain of S?

7. Supply of a product increases according to the model S(p) = a In(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 value of constants a and b in the supply function formula. (b) What is the mathematical domain of S? Is this different from the practical domain of S?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

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7. Supply of a product increases according to the model S(p) = a In(p – 6) 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 value of constants a and ò in the supply function formula.
(b) What is the mathematical domain of S? Is this different from the practical domain of S?

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