Question

I am not sure how to solve it.

The production of a manufacturer is given by the Cobb-Douglas production function

f(x,y)=30x^(3/5)y^(2/5)

where x represents the number of units of labor (in hours) and y
represents the number of units of capital (in dollars) invested.
Labor costs $15 per hour and there are 88 hours in a working day,
and 250 working days in a year. The manufacturer has allocated
$4,500,000 this year for labor and capital. How should the money be
allocated to labor and capital to maximize productivity this year?
Round answers to 2 decimal places, if necessary.

To maximize productivity, they should spend their money on ? hours
of labor and invest $?. This leads to a maximum value
of units. Also, if the number of dollars allocated to
labor and capital is increased by 11, the number of units produced
will (Select an answer) decrease increase by
approximately? .

Answer #1

The Cobb-Douglas production function for an automobile
manufacturer is
f(x, y) =
100x0.6y0.4,
where x is the number of units of labor and y
is the number of units of capital. Estimate the average production
level if the number of units of labor x varies between 300
and 350 and the number of units of capital y varies
between 375 and 400. (Round your answer to two decimal places.)

1. A. The Cobb-Douglas production function, f(x,y)=40x^1/4y^3/4,
describes the production of a company for which each unit of labor
costs $100 and each unit of capital costs $125. For a new project,
the company has allocated $60,000 for labor and capital. Find the
amount of money that the company should allocate to labor and
capital to maximize production.
B. The marketing department of a business has determined that
the demand for a product can be modeled by p=(50/(square root of...

Production The production function for a company is given by
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unit). The total cost for labor and capital cannot exceed
$100,000.
(a) Find the maximum production level for this manufacturer.
(Round your answer to the nearest integer.)
(b) Find the marginal productivity of money. (Round your answer
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Consider the Cobb-Douglas production function, f ( x , y ) = 50
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product produced using x units of labor and y
units of capital.
A. Compute the marginal productivities of labor and
capital when 32 unit of labor and 1 units of capital are
used.
B. Use the marginal productivities to approximate the
change in the number of units...

The production function for a company is given by
f(x, y) =
100x0.6y0.4
where x is the number of units of labor (at $48 per
unit) and y is the number of units of capital (at $36 per
unit). The total cost for labor and capital cannot exceed
$100,000.
(a)
Find the maximum production level for this manufacturer. (Round
your answer to the nearest integer.)
(b)
Find the marginal productivity of money. (Round your answer to
three decimal places.)
(c)...

Your automobile assembly plant has a Cobb-Douglas production
function given by
q =
100x0.3y0.7,
where q is the number of automobiles it produces per
year, x is the number of employees, and y is the
monthly assembly-line budget (in thousands of dollars). Annual
operating costs amount to an average of $60 thousand per employee
plus the operating budget of $12y thousand. Your annual
budget is $1,200,000. How many employees should you hire and what
should your assembly-line budget be to...

Suppose a Cobb-Douglas Production function is given by the
following:
P(L,K)=10L0.9K0.1
where L is units of labor, K is units of capital, and
P(L,K)P(L,K) is total units that can be produced with this
labor/capital combination. Suppose each unit of labor costs $400
and each unit of capital costs $1,200. Further suppose a total of
$600,000 is available to be invested in labor and capital
(combined).
A) How many units of labor and capital should be "purchased" to
maximize production subject...

Suppose a Cobb-Douglas Production function is given by the
following: P(L, K) = (50L^(0.5))(K^(0.5)) where L is units of
labor, K is units of capital, and P(L, K) is total units that can
be produced with this labor/capital combination. Suppose each unit
of labor costs $300 and each unit of capital costs $1,500. Further
suppose a total of $90,000 is available to be invested in labor and
capital (combined).
A) How many units of labor and capital should be "purchased"...

2. Assume that a manufacturer faces a Cobb-Douglas production
function, q=40K^0.5L^0.5
where q is output per period, L is labor, K is capital. The
market price of labor (w) is $50 per unit and the price of capital
(r) is $200 per unit.
a. Specify and illustrate graphically the short-run MPl and APl
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1. Suppose the equation p(x,y)=-2x^2+80x-3y^2+90+100 models
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(1) How many chairs and how many rockers will give the maximum
profit when there is not constraint?
(2) Due to an insufficient labor force they can only make a
total of 20 chairs and rockers per week (x + y = 20). So how many
chairs and how many rockers will give the...

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