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# Linear optimization for summary business problems

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A) Make a table that summarizes the above information.

b) Write down the optimization equation and the constraint equations and label them as such. Make sure your write down all of the constraint equations.

c) Graph, either by hand or using Excel, the constraint equations. Identify the feasible region. Make sure to label your graph.

d) Identify and determine the coordinates of ALL of the corner points on your graph.

e) Determine the amount of money you would make if you produced at each corner point. (Include ALL corner points.) Which corner point would you produce at? Why? How much money would you make? How many chairs and how many tables would you make?

#### Solution Preview

See the attached word document for the tables and graph.

Let's assign the following variables:
T = Number of tables made.
C = Number of chairs made.
P = Total profit margin.
L = Labor.
W = Wood.

Optimization equation:
Profit: 100T + 50C - Maximize profit.

Constraint equations:
Labor: 20T + 40C <= ...

#### Solution Summary

This problem utilizes linear optimization to determine the optimal production level given production constraints.

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