For the next group of exercises, use the method of Lagrange multipliers to solve the following applied problems. 393. [T] By investing x units of labor and y units of capital, a watch manufacturer can produce P ( x , y ) = 50 x 0.4 , y 0.6 watches. Find the maximum number of watches that can be produced on a budget of $20,000 if labor costs $100/unit and capital costs $200/ unit. Use a CAS to sketch a contour plot of the function.
For the next group of exercises, use the method of Lagrange multipliers to solve the following applied problems. 393. [T] By investing x units of labor and y units of capital, a watch manufacturer can produce P ( x , y ) = 50 x 0.4 , y 0.6 watches. Find the maximum number of watches that can be produced on a budget of $20,000 if labor costs $100/unit and capital costs $200/ unit. Use a CAS to sketch a contour plot of the function.
For the next group of exercises, use the method of Lagrange multipliers to solve the following applied problems.
393. [T] By investing x units of labor and y units of capital, a watch manufacturer can produce
P
(
x
,
y
)
=
50
x
0.4
,
y
0.6
watches. Find the maximum number of watches that can be produced on a budget of $20,000 if labor costs $100/unit and capital costs $200/ unit. Use a CAS to sketch a contour plot of the function.