5. Bess has hired Werner to plant trees. Bess derives a profit of p from each tree that is planted, and the cost to Werner of plantingt trees is C(t) (i) Suppose that Bess offers to pay Werner W(t) = A + Bt if he plants t trees. (A and B are constants, and B > 0.) How many trees will Werner plant? (ii) What is the value of Werner's profit in (i)? What is the value of Bess's profit? (iii) Suppose that Bess chooses values of A and B so that Werner receives a profit of zero. Among these combinations, which values of A and B maximize her profit and why? (iv) Suppose, instead, that Bess chooses A and B so that Werner receives a profit equal to Te* > 0. Which values of A and B will she choose?
5. Bess has hired Werner to plant trees. Bess derives a profit of p from each tree that is planted, and the cost to Werner of plantingt trees is C(t) (i) Suppose that Bess offers to pay Werner W(t) = A + Bt if he plants t trees. (A and B are constants, and B > 0.) How many trees will Werner plant? (ii) What is the value of Werner's profit in (i)? What is the value of Bess's profit? (iii) Suppose that Bess chooses values of A and B so that Werner receives a profit of zero. Among these combinations, which values of A and B maximize her profit and why? (iv) Suppose, instead, that Bess chooses A and B so that Werner receives a profit equal to Te* > 0. Which values of A and B will she choose?
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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Transcribed Image Text:5. Bess has hired Werner to plant trees. Bess derives a profit of p from each tree that is
t2
planted, and the cost to Werner of planting t trees is C(t) = .
2
(i) Suppose that Bess offers to pay Werner W(t) = A + Bt if he plants t trees. (A and B are
constants, and B > 0.) How many trees will Werner plant?
(ii) What is the value of Werner's profit in (i)? What is the value of Bess's profit?
(iii) Suppose that Bess chooses values of A and B so that Werner receives a profit of zero.
Among these combinations, which values of A and B maximize her profit and why?
(iv) Suppose, instead, that Bess chooses A and B so that Werner receives a profit equal to
T* > 0. Which values of A and B will she choose?
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