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

Step-by-step explanation:

We first denote the inequalities of the number of shirts and skirts.

#Since you cannot make a negative number of shirts or skirts, the inequalities will be written as:

#We then represent the inequality of material.

-The material size is a production constraint as only 500 yards of material is available for use.

-The inequality is therefore  written as:

#We then represent the inequality of time.

-The material size is a production constraint as only 800 hours available for use.

-The inequality is therefore  written as:

We combine the three inequalities to represent the constraints

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