A small company produces both dollhouses and sets of doll furniture. The dollhouses take 3 hours of labor to produce, and the furniture sets take 8 hours. The labor available is limited to 400 hours per week, and the total production capacity is 100 items per week. Existing orders require that at least 20 dollhouses and 10 sets of furniture be produced per week. Write a system of inequalities representing this situation, where x is the number of dollhouses and y is the number of furniture sets. Then graph the system of inequalities

Question

A small company produces both dollhouses and sets of doll furniture. The dollhouses take 3 hours of labor to produce, and the furniture sets take 8 hours. The labor available is limited to 400 hours per week, and the total production capacity is 100 items per week. Existing orders require that at least 20 dollhouses and 10 sets of furniture be produced per week. Write a system of inequalities representing this situation, where x is the number of dollhouses and y is the number of furniture sets. Then graph the system of inequalities

I am little confused but this what i am thinking this problem means
3x+8y=400
20x+10y=100
am i doing this right please let me know

First of all you need inequations, not equations

your first one is 3x+8y ≤ 400

The production limit of 100 items would translate to
x+y ≤ 100

at least 20 dollhouses ---> x ≥ 20
at least 10 furniture ----> y ≥ 10

3.09(j+4.6)=

How do you graph this?

how about math work word problems

Answer 1

you write good math problems and by the way how old are you

Answer 2

i don't know....... that why i asking

Answer 3

To graph a system of inequalities, you need to plot the lines that represent each inequality and shade the region that satisfies all the inequalities.

Let's start by graphing the first inequality: 3x + 8y ≤ 400.

To graph this inequality, we need to rewrite it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Rearranging the inequality, we have:
8y ≤ -3x + 400
y ≤ (-3/8)x + 50

Now we can plot the line y = (-3/8)x + 50 on a graph by finding two points on the line:

When x = 0, y = 50
When x = 200, y = 0

Plot these two points and draw a line passing through them.

Next, let's graph the second inequality: x + y ≤ 100.

Rearranging the inequality, we get:
y ≤ -x + 100

To graph this line, let's again find two points on the line:

When x = 0, y = 100
When x = 100, y = 0

Plot these two points and draw a line passing through them.

Now, let's include the remaining two inequalities: x ≥ 20 and y ≥ 10.

For x ≥ 20, draw a vertical line through x = 20. Shade the area to the right of this line.

For y ≥ 10, draw a horizontal line through y = 10. Shade the area above this line.

The shaded region where all the lines intersect represents the feasible solutions to the system of inequalities.