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.

C) x ≥ 0 and y ≥ 0

0.5x + y ≤ 500

x + 1.5y ≤ 800

Step-by-step 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

step-by-step explanation:

∆abc has the points a(1, 7), b(-2, 2), and c(4, 2) as its vertices. formed with the point d(1, 2) as its third vertex, then ∆abd is triangle.

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