Two women have decided to start a cottage industry that will be run out of their homes. They are going to make two types of specialty shirts, rhinestone and embroidery. The total gross profit is given by P(x, y) = 16x + 20y – x² – y² where x is the number of rhinestone shirts made and y is the number of embroidery shirts made per month. Together, they are able to make at most a total of six shirts per month. What is the number of each type of shirt that they should try to make and sell in order to maximize their profit each month? Solve using Lagrange multipliers approach.
Two women have decided to start a cottage industry that will be run out of their homes. They are going to make two types of specialty shirts, rhinestone and embroidery. The total gross profit is given by P(x, y) = 16x + 20y – x² – y² where x is the number of rhinestone shirts made and y is the number of embroidery shirts made per month. Together, they are able to make at most a total of six shirts per month. What is the number of each type of shirt that they should try to make and sell in order to maximize their profit each month? Solve using Lagrange multipliers approach.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![Two women have decided to start a cottage industry that will be run out of their
homes. They are going to make two types of specialty shirts, rhinestone and embroidery. The
total gross profit is given by P(x, y) = 16x + 20y – x² – y² where x is the number of
rhinestone shirts made and y is the number of embroidery shirts made per month. Together,
they are able to make at most a total of six shirts per month. What is the number of each type
of shirt that they should try to make and sell in order to maximize their profit each month? Solve
using Lagrange multipliers approach.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd892d11f-8a6e-4f28-b288-d5b1f25d8311%2F683a84a2-7120-4b3d-889e-0688e86c2d83%2Fdwade_processed.png&w=3840&q=75)
Transcribed Image Text:Two women have decided to start a cottage industry that will be run out of their
homes. They are going to make two types of specialty shirts, rhinestone and embroidery. The
total gross profit is given by P(x, y) = 16x + 20y – x² – y² where x is the number of
rhinestone shirts made and y is the number of embroidery shirts made per month. Together,
they are able to make at most a total of six shirts per month. What is the number of each type
of shirt that they should try to make and sell in order to maximize their profit each month? Solve
using Lagrange multipliers approach.
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