SOLUTION: A small company produces both standard and deluxe playhouses. The standard playhouses take 12 hours of labor to produce, and the deluxe playhouses take 20 hours. The labor availa
Question 72934: A small company produces both standard and deluxe playhouses. The standard playhouses take 12 hours of labor to produce, and the deluxe playhouses take 20 hours. The labor available is limited to 800 hours per week, and the total production capacity is 50 items per week. Existing orders require the company to produce at least 10 standard playhouses and 15 deluxe playhouses per week. Write a system of inequalities representing this situation, where x is the number of standard playhouses and y is the number of deluxe playhouses. Then graph the system of inequalities. Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! A small company produces both standard (let # be x) and deluxe (let # be y) playhouses.
-------------
The standard playhouses take 12 hours of labor to produce, and the deluxe playhouses take 20 hours.
The labor available is limited to 800 hours per week,
Labor Inequality: 12x + 20y <=800
--------------
and the total production capacity is 50 items per week.
Capacity Inequality: x + y <=50
---------------
Existing orders require the company to produce at least 10 standard playhouses and 15 deluxe playhouses per week.
x >= 10
y >= 15
-------------
Write a system of inequalities representing this situation, where x is the number of standard playhouses and y is the number of deluxe playhouses.
------------
Then graph the system of inequalities.
Solve the inequalities for y:
Labor Inequality y <= (-3/5)x+40
Capacity Inequl y <= -x+50
Note: x >= 10 tells you the Domain for the solution set.
y >=15 tells you the Range for the solution set.
------------
Graph the EQUALITIES: y=(-3/5)x+40; y=-x+50 to determine the boundaries of the solution set.
The solution is the intersection of the inequality and equality sets
=============
Cheers,
Stan H.
(