a.
To describe: The system of inequalities that represent the number of chairs and tables.
a.
Answer to Problem 15PT
The system of inequalities that represent the number of chairs and tables is
Explanation of Solution
Given information:
The processing to make a table and chair is provided below,
108 hours of carpentry and 20 hours of finishing per day are available. The profit for a table is $35 and for chair is $25.
Calculation:
Consider the provided information thatprocessing to make a table and chair is provided below,
108 hours of carpentry and 20 hours of finishing per day are available. The profit for a table is $35 and for chair is $25.
Let c denote the number of chairs and y denote the number of tables.
The constraints are,
The objective function is,
b.
To graph: The region that depicts the possible number of chair and table manufactured.
b.
Explanation of Solution
Given information:
The system of inequalities that represent the number of chairs and tables is
Graph:
Consider the provided information system of inequalities that represent the number of chairs and tables is
Plot the above inequalities on coordinate plane.
Interpretation:
The shaded region represents the feasible. It is a quadrilateral with 4 corner points.
c.
To calculate:The number of chairs and tables to maximize the profit.
c.
Answer to Problem 15PT
The maximum profit is $700 which is when no chair and 20 tables are made.
Explanation of Solution
Given information:
The processing to make a table and chair is provided below,
108 hours of carpentry and 20 hours of finishing per day are available. The profit for a table is $35 and for chair is $25.
Calculation:
Consider the provided information thatprocessing to make a table and chair is provided below,
108 hours of carpentry and 20 hours of finishing per day are available. The profit for a table is $35 and for chair is $25.
Let c denote the number of chairs and y denote the number of tables.
The constraints are,
The objective function is,
Plot the above inequalities on coordinate plane.
The profit function that is the cost function that is to be maximized is
Substitute the vertices of the feasible region to find the point at which maximum revenue is there.
Substitute
Substitute
Substitute
Substitute
Since, maximum profit is $700 which is when no chair and 20 tables are made.
Chapter 3 Solutions
Algebra 2
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