Based on the following: i: x ≥0 ii: y ≥0 iii: z ≥0 iv: 0.5x + y + 0.2x ≥ 600 v: 2.0x + 3y + z ≤ 2000 I am confused how one gets the following coordinate - 1#4#5: (0, 500, 500) ------------------------ When x = 0 (x greater than or equal to zero), we get our fourth and fifth equation as 0.5(0)+y+0.2z=600 2.0(0)+3y+z=2000 y+0.2z = 600 3y+z = 2000 solving these two equations for y and z we get y = 500 and z = 500, so the coordinates are (0, 500, 500) -------------------------------- What is the calculation behind (0, 500, 500)? Need the breakdown on how from y+0.2z = 600 and 3y+z = 2000, the coordinates (0, 500, 500) came. Thank you.

Based on the following: i: x ≥0 ii: y ≥0 iii: z ≥0 iv: 0.5x + y + 0.2x ≥ 600 v: 2.0x + 3y + z ≤ 2000 I am confused how one gets the following coordinate - 1#4#5: (0, 500, 500) ------------------------ When x = 0 (x greater than or equal to zero), we get our fourth and fifth equation as 0.5(0)+y+0.2z=600 2.0(0)+3y+z=2000 y+0.2z = 600 3y+z = 2000 solving these two equations for y and z we get y = 500 and z = 500, so the coordinates are (0, 500, 500) -------------------------------- What is the calculation behind (0, 500, 500)? Need the breakdown on how from y+0.2z = 600 and 3y+z = 2000, the coordinates (0, 500, 500) came. Thank you.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.1: Equations

Problem 58E

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Concept explainers

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

Question

Based on the following:
i: x ≥0
ii: y ≥0
iii: z ≥0
iv: 0.5x + y + 0.2x ≥ 600
v: 2.0x + 3y + z ≤ 2000

I am confused how one gets the following coordinate -

1#4#5: (0, 500, 500)

------------------------

When x = 0 (x greater than or equal to zero), we get our fourth and fifth equation as

0.5(0)+y+0.2z=600

2.0(0)+3y+z=2000

y+0.2z = 600

3y+z = 2000

solving these two equations for y and z we get y = 500 and z = 500, so the coordinates are (0, 500, 500)

--------------------------------

What is the calculation behind (0, 500, 500)? Need the breakdown on how from y+0.2z = 600 and 3y+z = 2000, the coordinates (0, 500, 500) came.

Thank you.

TABLE 4-3
Corner
Co-ordinates
Check
0 - z+ 4y +3z
142#3
1#244
1#245
1434
1#3#5
14445
243#4
2#3#5
244#5
3#445
(0, 0, 0)
(0, 0, 3,000)
(0, 0, 2,000)
(0, 600, 0)
(0, 2,000/3, 0)
(0, 500, 500)
(1,200, 0, 0)
(1,000, 0, 0)
(2,000, 0, -2,000)
(400, 400, 0)
No
No
No
Yes
Yes
Yes
No
No
No
Yes
2,400
8,000/3
3,500
2,000*
• Indicates the minimum.

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