Whoville Marble Works (WMW) produces Bespoke Marble Kits (BMKs) for discerningmarble connoisseurs. To produce their BMKS, WMW uses raw materials, labor and energy,and their production function is given by q = 2070-410.250.35, whereo q = WMW's monthly output, measured in BMKS,or = WMW's monthly raw material input, measured in tons,• 1 = WMW's monthly labor input, measured in hours of labor,• m = WMW's monthly energy input, measured in megawatt hours.Raw material costs WMW $100/ton, labor costs WMW $30/hour and energy costs WMW$50/megawatt hour.Find the input levels of raw materials, labor and energy that maximize WMW's output, giventhat their monthly production budget is $30,000. What is the minimum cost?

The production function shows the relationship between inputs and output. The increase in inputs…

Whoville Marble Works (WMW) produces Bespoke Marble Kits (BMKs) for discerning marble connoisseurs. To produce their BMKS, WMW uses raw materials, labor and energy, and their production function is given by q=2070.410.25 m 0.35, where

Whoville Marble Works (WMW) produces Bespoke Marble Kits (BMKs) for discerning marble connoisseurs. To produce their BMKS, WMW uses raw materials, labor and energy, and their production function is given by q=2070.410.25 m 0.35, where

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.9P

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Question

Whoville Marble Works (WMW) produces Bespoke Marble Kits (BMKs) for discerning
marble connoisseurs. To produce their BMKS, WMW uses raw materials, labor and energy,
and their production function is given by q = 2070-410.250.35, where
o q = WMW's monthly output, measured in BMKS,
or = WMW's monthly raw material input, measured in tons,
• 1 = WMW's monthly labor input, measured in hours of labor,
• m = WMW's monthly energy input, measured in megawatt hours.
Raw material costs WMW $100/ton, labor costs WMW $30/hour and energy costs WMW
$50/megawatt hour.
Find the input levels of raw materials, labor and energy that maximize WMW's output, given
that their monthly production budget is $30,000. What is the minimum cost?

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