Question

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

Answer 1

x ≥ 0 and y ≥ 0

0.5x + y ≤ 500

x + 1.5y ≤ 800

When graphed the system shows that the manufacturer should make 200 shirts and 400 skirts for a maximum profit.

so the answer is C

Explanation:

Answer 2

`C.\ \ \ \\\\\x\geq 0\ \ \ ,y\geq 0\\\\0.5x+y\leq 500\\\\x+1.5y\leq 800`

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:

`Shirts=> x\geq 0\\\\skirts=>y\geq 0`

#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:

`x \ takes \ 0.5\ yards\\y\ takes \ 1 \ yard\\\\\therefore 0.5x+y\leq 500`

#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:

`x \ takes\ 1 \ hr\\y \ takes\ 1.5 \ hr\\\\\therefore x+1.5y\leq 800`

We combine the three inequalities to represent the constraints

`x\geq 0\ \ \ ,y\geq 0\\\\0.5x+y\leq 500\\\\x+1.5y\leq 800`