Answer:
(D) The intersection of two half planes.
Step-by-step explanation:
In order to solve the two order inequality, the two equations to be solved divides the cartesian plane into two half planes.
The intersection of the two inequalities gives the set of the points that satisfies both the inequalities. Thus, the solution of the two order inequality can be obtained by the intersection of the two half planes.
Which triangles am I supposed to choose from?
The numbers of chairs and tables that should be produced each week in order to maximize the company's profit is 15 chairs and 18 tables.
Since a furniture company has 480 board ft of teak wood and can sustain up to 450 hours of labor each week, and each chair produced requires 8 ft of wood and 12 hours of labor, and each table requires 20 ft of wood and 15 hours of labor, to determine, if a chair yields a profit of $ 65 and a table yields a profit of $ 90, what are the numbers of chairs and tables that should be produced each week in order to maximize the company's profit, the following calculation should be done:
16 chairs; 24 tables
Time used = 16 x 12 + 24 x 15 = 192 + 360 = 552
Wood used = 16 x 8 + 24 x 20 = 128 + 480 = 608
15 chairs; 18 tables
Time used = 15 x 12 + 18 x 15 = 180 + 270 = 450
Wood used = 15 x 8 + 18 x 20 = 120 + 360 = 480
12 chairs; 28 tables
Time used = 12 x 12 + 28 x 15 = 144 + 420 = 564
Wood used = 12 x 8 + 28 x 20 = 96 + 540 = 636
18 chairs; 20 tables
Time used = 18 x 12 + 20 x 15 = 216 + 300 = 516
Wood used = 18 x 8 + 20 x 20 = 144 + 400 = 544
Therefore, the only option that meets the requirements of time and wood used is that of 15 chairs and 18 tables, whose economic benefit will be the following:
15 x 65 + 18 x 90 = X
975 + 1,620 = X
2,595 = X
Therefore, the numbers of chairs and tables that should be produced each week in order to maximize the company's profit is 15 chairs and 18 tables.
Answer:
Volume of the pyramid = 16m³ or 16 cubic meters.
Step-by-step explanation:
The equation for the volume of a pyramid is:
where b = area of base and h = height.
In this case, the base is a square with a side length of 4m.
Area of the square base = (4m)² = b = 16m²
h = 3m
Insert b and a into the volume of a pyramid equation.
= 16m³
Volume of the pyramid = 16m³ or 16 cubic meters.
A=length x height. First we want to know the area of the original sheet of paper. 8.5 x 11= 93.5 inches squared. Then we take two squares with side length 2 inches. The area of each of these squares is 2 x 2, or 4 inches. Since there are two, the total area we take away is 8 inches. We subtract 8 inches from 93.5 since we took it away, and the final area of the paper is 85.5 inches^{2}
Hope this helped!
