Answer:
C) x ≥ 0 and y ≥ 0
0.5x + y ≤ 500
x + 1.5y ≤ 800
Explanation:
A children clothing manufacturer has 500 yards of material to make shirts and skirts. A shirt requires 0.5 yards of fabric, and a skirt requires 1 yard of fabric. It takes 1 hour to make a shirt and 1.5 hours to make a skirt. The manufacture has 800 hours available to make shirts and skirts.
Which system of inequalities represent the constraints for this situation? Let x = number of shirts, and let y = number of skirts.
A) x ≤ 0 and y ≤ 0
0.5x + y ≤ 800
x + 1.5y ≤ 500
B) x ≤ 0 and y ≤ 0
0.5x + y ≥ 800
x + 1.5y ≥ 500
C) x ≥ 0 and y ≥ 0
0.5x + y ≤ 500
x + 1.5y ≤ 800
D) x ≥ 0 and y ≥ 0
0.5x + y ≥ 500
x + 1.5y ≥ 800
number of shirts,x and number of skirts,y must be greater than 0 since it can not be a negative value
x ≥ 0 ; y ≥ 0
Inequality for number of yards
x = 0.5 yards ; y = 1 yard
Total yards = 500
The inequality is
0.5x + y ≤ 500
Inequality for hours of production
x = 1 hour ; y = 1.5 hours
Total available hours for production = 800
The inequality is
x + 1.5y ≤ 800
Therefore, the system of inequalities which represent the constraints for this situation is
x ≥ 0 ; y ≥ 0
0.5x + y ≤ 500
x + 1.5y ≤ 800