Homework SourseA manager has been allotted 8000 to spend on the development
A manager has been allotted $8000 to spend on the development and promotion of a new product. It is estimated that if x thousand dollars are spent on development and y thousand dollars on promotion, approximately f(x,y)=74x^(1/2)*y^(3/2) units of the product will be sold.
a) How much money should the editor allocate to development and how much to promotion in order to maximize sales?
Development (x):
Promotion (y):
a) How much money should the editor allocate to development and how much to promotion in order to maximize sales?
Development (x):
Promotion (y):
Solution
x+y = 8000
Maximize f(x,y)
We have:
f(x,y) = 74x^(1/2)*y^(3/2) = 74x^(1/2)*(8000-x)^(3/2)
df/dx = 74(1/2 x^(-1/2)(8000-x)^(3/2) - (3/2)x^(1/2)(8000-x)^(1/2)) = 0
37x^(-1/2)(8000-x)^(1/2) (8000-x-3x) = 0
8000-4x = 0
x = 8000/4 = 2000
y = 8000 - x = 6000
Thus:
Development (x): 2000
Promotion (y): 6000
