Math156_Lab_4

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Brookdale Community College *

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156

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Mathematics

Date

Apr 3, 2024

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pdf

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2

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07/2020 MATH 156 S ECTION 4.3, 4.4 M EMBERS OF G ROUP : There are many websites that will do linear optimization for you using the Simplex method. We will be using: http://zweigmedia.com/RealWorld/simplex.html 1. After Hurricane Katrina, one of the housing solutions was to build modular homes. One contractor builds two types of homes: the Carolina requires $110,000 in capital and 180 worker-days of labor, while the Savannah requires $240,000 in capital and 120 worker-days of labor. The contractor has at most $48,000,000 available capital and no more than 43,200 worker-days of labor available. The company’s profit is $45,000 on the Carolina and $60,000 on the Savannah . How many of each type of home should the company build to maximize profit? (a) Define each variable as a complete sentence. (b) Write the objective and objective function. (c) List the constraint inequalities. (d) Use the online simplex program to find the optimal solution. Write the solution here. (e) Interpret the result of (d) in the context of this situation as a complete sentence.
2. CDF Appliances has assembly plants in Atlanta and Fort Worth where it produces a variety of kitchen appliances, including a 12-cup coffee maker and a cappuccino machine. In each hour at the Atlanta plant, 160 of the 12 cup models and 200 of the cappuccino machines can be assembled, and the hourly cost is $700. In each hour at the Fort Worth plant, 800 of the 12 cup machines can be assembled and 200 of the cappuccino machines can be assembled, and the hourly cost is $2100. CDF Appliances expects orders each week for at least 64000 of the 12 cup models and at least 40000 of the cappuccino machines. How many hours per week should each plant be operating in order to provide inventory for the orders at minimum cost? Find the minimum cost. (a) Define each variable as a complete sentence. (b) Write the objective and objective function. (c) List the constraint inequalities. (d) Use the online simplex program to find the optimal solution. Write the solution here. (e) Interpret the result of (d) in the context of this situation as a complete sentence.
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