1. ## LINEAR PROGRAMING.

A garment company makes two types of woolen sweaters and can produce a max of 700 sweaters per week. Each sweater of the first type requires 2 pounds of green wool and 4 pounds of pink wool to produce a single sweater. The second type of sweater requires 4 pounds of green wool and 3 pounds of pink wool. The profit earned the first type of sweater is $5 and on the second type$7 . The company has 50 ounds of green wool and 80 pound of pink wool.

Write a system of inequalities to represent the number of sweaters of the first type and the number of sweaters of the second type that can be produced.

2. Originally Posted by dreamgirl
A garment company makes two types of woolen sweaters and can produce a max of 700 sweaters per week. Each sweater of the first type requires 2 pounds of green wool and 4 pounds of pink wool to produce a single sweater. The second type of sweater requires 4 pounds of green wool and 3 pounds of pink wool. The profit earned the first type of sweater is $5 and on the second type$7 . The company has 50 ounds of green wool and 80 pound of pink wool.

Write a system of inequalities to represent the number of sweaters of the first type and the number of sweaters of the second type that can be produced.

Hello dreamgirl,

Let x = number of type 1
Let y = number of type 2

1st constraint: $\displaystyle \boxed{x+y\leq 700}$

2nd constraint: $\displaystyle \boxed{2x+4y\leq 50}$ Green wool

3rd constraint: $\displaystyle \boxed{4x+3y\leq 80}$ Pink wool

4th constraint: $\displaystyle \boxed{x\ge 0}$

5th constraint: $\displaystyle \boxed{y\ge 0}$

Profit function: $\displaystyle P(x, y)=5x+7y$