The Wellbuilt Company produces two types of wood chippers, economy and deluxe. The deluxe model requires 3 hours to assemble and 1/2 hour to paint, and the economy model requires 2 hours to assemble and 1 hour to paint. The maximum number of assembly hours available is 18 per day, and the maximum number of painting hours available is 7 per day.
The Wellbuilt Company produces two types of wood chippers, economy and deluxe. The deluxe model requires 3 hours to assemble and 1/2 hour to paint, and the economy model requires 2 hours to assemble and 1 hour to paint. The maximum number of assembly hours available is 18 per day, and the maximum number of painting hours available is 7 per day.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter6: Systems Of Linear Equations And Inequalities
Section6.6: Systems Of Inequalities
Problem 44PFA
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Question
The Wellbuilt Company produces two types of wood chippers, economy and deluxe. The deluxe model requires 3 hours to assemble and 1/2 hour to paint, and the economy model requires 2 hours to assemble and 1 hour to paint. The maximum number of assembly hours available is 18 per day, and the maximum number of painting hours available is 7 per day.
(a) Write the system of inequalities that describes the constraints on the number of each type of wood chipper produced. (Let x represent the number of deluxe models, and let y represent the number of economy models.)
(b) Graph the solution of the system of inequalities.
Find the corners of the solution region. (Order your answers from smallest to largest x, then from smallest to largest y.)
|
3x+2y≤18
|
assembly time constraint | |
|
x+2y≤14
|
painting time constraint | |
| x ≥ 0 | production constraint, deluxe | |
| y ≥ 0 | production constraint, economy |
(b) Graph the solution of the system of inequalities.
Selection Tool
Find the corners of the solution region. (Order your answers from smallest to largest x, then from smallest to largest y.)
| (x, y) | = |
2,6
|
||
| (x, y) | = |
6,14
|
||
| (x, y) | = |
6,9
|
||
| (x, y) | = |
|
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