Thread: Inequalities Problem..

This question really stumpted me><...i am really confused, can anyone help me?

Production Choices: The following system of inequalities models the restrictions on the number x of wooden table chairs and the number y of wooden rocking chairs made at a furniture factory each week. These restrictions are caused by limitations on the factory's equipment and labor supply

x>0
y>0
x+y<50
3x+y<90

**All the greater and less than signs are "equal" so, for the first one it's x is greater than and equal to 0. (i dont know how to do the mathematical sign)**

a) Determine each corner point of the region formed by graphing this system of inequalities.
b) The factory makes $20 for each table chair and $25 for each rocking chair. Write an expression for the priofit involving x and y
c) Evaluate the profit expression from part b at each of the corner points from part a. Which of these points produces the greates profit for the factory?

x >= 0 ------------(1)
y >= 0 ------------(2)
x+y <= 50 ---------(3)
3x+y <= 90 --------(4)

a) Determine each corner point of the region formed by graphing this system of inequalities.

There are four inequalities so there should be four corner points.
P1 = intersection of inequalities (1) and (2) = (0,0)
P2 = intersection of inequalities (2) and (3) = (0,50)
P3 = intersection of inequalities (3) and (4) = (20,30)
P4 = intersection of inequalities (4) and (1) = (30,0)

b) The factory makes $20 for each table chair and $25 for each rocking chair. Write an expression for the priofit involving x and y

P = x(20) +y(30)
P = 20x +30y --------------in dollars.

c) Evaluate the profit expression from part b at each of the corner points from part a. Which of these points produces the greates profit for the factory?

In P1 (0,0)-----P = 20(0) +30(0) = 0
In P2 (0,50)----P = 20(0) +30(50) = $1500
In P3 (20,30)---P = 20(20) +30(30) = 400 +900 = $1300
In P4 (30,0)---P = 20(30) +30(0) = $600

The point (0,50) produces the greatest profit.